diff --git a/changelog b/changelog index 509310d..a244a50 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,4 @@ +20080408 tpd src/input/mapleok.input fix I->%i, reorganize 20080406 tpd src/input/Makefile add integration regression testing 20080406 tpd src/input/schaum19.input integrals of sin(ax) and cos(ax) 20080404 tpd faq FAQ 46: Axiom Trademark information diff --git a/src/input/mapleok.input.pamphlet b/src/input/mapleok.input.pamphlet index 1fb777d..a470496 100644 --- a/src/input/mapleok.input.pamphlet +++ b/src/input/mapleok.input.pamphlet @@ -19,7 +19,7 @@ )set message auto off )clear all )set break resume ---S 1 of 267 +--S 1 of 224 in1012a:=integrate(log(abs(z^3-1))/(1+z)^2, z= 0..%plusInfinity,"noPole") --R --R @@ -30,43 +30,27 @@ in1012a:=integrate(log(abs(z^3-1))/(1+z)^2, z= 0..%plusInfinity,"noPole") --R Type: Union(f1: OrderedCompletion Expression Integer,...) --E 1 ---S 2 of 267 -in101a:=integrate((sqrt(z)^I)^I, z= 0..1,"noPole") +--S 2 of 224 +in101a:=integrate((sqrt(z)^%i)^%i, z= 0..1,"noPole") --R --R ---R 2 ---R (2) ------ ---R 2 ---R I + 2 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) +--R (2) 2 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) --E 2 ---S 3 of 267 -in106a:=integrate(((I+z)^I)^I, z= 0..1,"noPole") ---R ---R ---R 2 2 ---R I log(I + 1) I log(I) ---R (I + 1)%e - I %e ---R (3) ------------------------------------ ---R 2 ---R I + 1 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 3 - ---S 4 of 267 +--S 3 of 224 in108a:=integrate(sqrt((1 + cos(z))*(1 + sin(z))),z=0..%plusInfinity,"noPole") --R --R ---R (4) + infinity +--R (3) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 4 +--E 3 ---S 5 of 267 +--S 4 of 224 in119a:=integrate(log(1/z+sqrt(1+1/z)), z=0..1,"noPole") --R --R ---R (5) +--R (4) --R +-+ +-+ +-+ --R 3log(2\|2 + 3) + 2log(\|2 + 1) - 3log(- 2\|2 + 3) --R + @@ -78,129 +62,67 @@ in119a:=integrate(log(1/z+sqrt(1+1/z)), z=0..1,"noPole") --R / --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 5 +--E 4 ---S 6 of 267 +--S 5 of 224 in120a:=integrate(1/(1+1/z^6), z=0..%plusInfinity) --R --R ---R (6) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 6 - ---S 7 of 267 -in1029a:=integrate((I*z/(I*z+1))^(1/2), z= 0..%plusInfinity,"noPole") ---R ---R ---R (7) + infinity +--R (5) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 7 +--E 5 ---S 8 of 267 -in1030a:=integrate(I*z/(I*z+1), z= 0..%plusInfinity,"noPole") +--S 6 of 224 +in1030a:=integrate(%i*z/(%i*z+1), z= 0..%plusInfinity,"noPole") --R --R ---R (8) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 8 +--R (6) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 6 ---S 9 of 267 +--S 7 of 224 in1066a:=integrate(acoth(z)*real(z), z= 0..1,"noPole") --R --R --R 1 ---R (9) - +--R (7) - --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 9 +--E 7 ---S 10 of 267 +--S 8 of 224 in1067a:=integrate(acoth(z)*z^(1/2), z= 0..1,"noPole") --R --R ---R - 2log(2) - %pi + 8 ---R (10) ------------------- ---R 6 +--R - 2log(2) - %pi + 8 +--R (8) ------------------- +--R 6 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 10 +--E 8 ---S 11 of 267 +--S 9 of 224 in1076a:=integrate(sin(z)*(1-cos(z)/(1-sin(z)^2)^(1/2))^2, z= 0..1,"noPole") --R --R ---R (11) - 4cos(1) + 4 +--R (9) - 4cos(1) + 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 11 +--E 9 ---S 12 of 267 +--S 10 of 224 in1084a:=integrate(atan(sin(z))+atan(1/sin(z)), z= 0..1,"noPole") --R --R --R %pi ---R (12) - --- +--R (10) - --- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 12 - ---S 13 of 267 -in1107a:=integrate(-log(z)/(-1+z^(1/2))^3, z= 0..1/2*I,"noPole") ---R ---R ---R (13) ---R +-+ ---R +-+ +-+ \|I ---R ((2I + 12)\|I + (- 6I - 4)\|2 )log(----) ---R +-+ ---R \|2 ---R + ---R +-+ +-+ ---R +-+ +-+ - 4\|I + (I + 2)\|2 ---R ((- I - 6)\|I + (3I + 2)\|2 )log(---------------------) ---R +-+ ---R 2\|2 ---R + ---R 2 2 ---R I +-+ +-+ I +-+ ---R (- 3log(--) + 2I + 4)\|I + (I + 1)\|2 log(--) - 4I\|2 ---R 4 4 ---R / ---R +-+ +-+ ---R (I + 6)\|I + (- 3I - 2)\|2 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 13 - ---S 14 of 267 -in1108a:=integrate(log(z)/(-1+z^(1/2))^3, z= 0..1/2*I,"noPole") ---R ---R ---R (14) ---R +-+ ---R +-+ +-+ \|I ---R ((- 2I - 12)\|I + (6I + 4)\|2 )log(----) ---R +-+ ---R \|2 ---R + ---R +-+ +-+ ---R +-+ +-+ - 4\|I + (I + 2)\|2 ---R ((I + 6)\|I + (- 3I - 2)\|2 )log(---------------------) ---R +-+ ---R 2\|2 ---R + ---R 2 2 ---R I +-+ +-+ I +-+ ---R (3log(--) - 2I - 4)\|I + (- I - 1)\|2 log(--) + 4I\|2 ---R 4 4 ---R / ---R +-+ +-+ ---R (I + 6)\|I + (- 3I - 2)\|2 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 14 +--E 10 ---S 15 of 267 +--S 11 of 224 in1112a:=integrate((1-1/z)^(1/2), z= %pi..2*%pi,"noPole") --R --R ---R (15) +--R (11) --R +--------+ +-------+ --R |2%pi - 1 |%pi - 1 --R - 2log( |-------- + 1) + 2log( |------- + 1) @@ -220,198 +142,130 @@ in1112a:=integrate((1-1/z)^(1/2), z= %pi..2*%pi,"noPole") --R / --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 15 +--E 11 ---S 16 of 267 -in1114a:=integrate(-z-(1/2*2^(1/2)+1/2*I*2^(1/2))*z^(1/2), z= 1..%plusInfinity,"noPole") +--S 12 of 224 +in1114a:=integrate(-z-(1/2*2^(1/2)+1/2*%i*2^(1/2))*z^(1/2), z= 1..%plusInfinity,"noPole") --R --R ---R (16) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 16 +--R (12) - infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...) +--E 12 ---S 17 of 267 -in1118:=integrate(acot(z), z= 0..1/2*I) +--S 13 of 224 +in1118:=integrate(acot(z), z= 0..1/2*%i) --R --R ---R 2 ---R I + 4 4I ---R 2log(------) + I atan(------) ---R 4 2 ---R I - 4 ---R (17) ----------------------------- ---R 4 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 17 +--R 1 3 1 1 +--R (13) - log(-) - - log(-) +--R 2 4 8 9 +--R Type: Union(f1: OrderedCompletion Expression Complex Fraction Integer,...) +--E 13 ---S 18 of 267 +--S 14 of 224 in1120a:=integrate((z^2)^(1/2), z= 1..2,"noPole") --R --R --R 3 ---R (18) - +--R (14) - --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 18 - ---S 19 of 267 -in1130a:=integrate(3^log(z), z= -I..I,"noPole") ---R ---R ---R log(3)log(I) log(3)log(- I) ---R I %e + I %e ---R (19) ------------------------------------- ---R log(3) + 1 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 19 +--E 14 ---S 20 of 267 -in1149:=integrate(imag(z)*z^(1/6), z= -I..I) +--S 15 of 224 +in1130a:=integrate(3^log(z), z= -%i..%i,"noPole") --R --R ---R (20) 0 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 20 +--R log(%i)log(3) log(- %i)log(3) +--R %i %e + %i %e +--R (15) ----------------------------------------- +--R log(3) + 1 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 15 ---S 21 of 267 +--S 16 of 224 in1149:=integrate(imag(z)*z^(1/6), z= -%i..%i) --R --R ---R (21) 0 +--R (16) 0 --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 21 - ---S 22 of 267 -in1150a:=integrate(1/z^(1/2), z= -I..I,"noPole") ---R ---R ---R +-+ +---+ ---R (22) 2\|I - 2\|- I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 22 +--E 16 ---S 23 of 267 -in1150c:=integrate(1/z^(1/2), z= -%i..%i,"noPole") +--S 17 of 224 +in1150a:=integrate(1/z^(1/2), z= -%i..%i,"noPole") --R --R --R +--+ +----+ ---R (23) 2\|%i - 2\|- %i +--R (17) 2\|%i - 2\|- %i --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 23 - ---S 24 of 267 -in1161:=integrate(hermiteH(1, z), z= -I..I) ---R ---R ---R (24) 0 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 24 +--E 17 ---S 25 of 267 +--S 18 of 224 in1161a:=integrate(hermiteH(1, z), z= -%i..%i) --R --R ---R (25) 0 +--R (18) 0 --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 25 - ---S 26 of 267 used to work -in1160:=integrate(HermiteH(2, z), z= -%i..%i) ---R ---R There are no library operations named HermiteH ---R Use HyperDoc Browse or issue ---R )what op HermiteH ---R to learn if there is any operation containing " HermiteH " in its ---R name. ---R ---RDaly Bug ---R Cannot find a definition or applicable library operation named ---R HermiteH with argument type(s) ---R PositiveInteger ---R Variable z ---R ---R Perhaps you should use "@" to indicate the required return type, ---R or "$" to specify which version of the function you need. ---E 26 --- --- 20%i --- - ---- --- 3 --- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 18 ---S 27 of 267 -in1162:=integrate(laguerreL(1, z), z= -I..I) +--S 19 of 224 +in1160:=integrate(hermiteH(2, z), z= -%i..%i) --R --R ---R (26) 2I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 27 +--R 20%i +--R (19) - ---- +--R 3 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 19 ---S 28 of 267 +--S 20 of 224 in1162:=integrate(laguerreL(1, z), z= -%i..%i) --R --R ---R (27) 2%i +--R (20) 2%i --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 28 - ---S 29 of 267 -in1163:=integrate(legendreP(3, z), z= -I..I) ---R ---R ---R (28) 0 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 29 +--E 20 ---S 30 of 267 +--S 21 of 224 in1163:=integrate(legendreP(3, z), z= -%i..%i) --R --R ---R (29) 0 +--R (21) 0 --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 30 - ---S 31 of 267 -in1164:=integrate(legendreP(2, z), z= -I..I) ---R ---R ---R 3 ---R (30) I - I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 31 +--E 21 ---S 32 of 267 +--S 22 of 224 in1164:=integrate(legendreP(2, z), z= -%i..%i) --R --R ---R (31) - 2%i +--R (22) - 2%i --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 32 +--E 22 ---S 33 of 267 +--S 23 of 224 in1167a:=integrate((z^2)^(1/6), z= -3..-1,"noPole") --R --R --R 3+---+ 3+---+ --R - 3\|- 1 + 9\|- 3 ---R (32) ------------------- +--R (23) ------------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 33 +--E 23 ---S 34 of 267 +--S 24 of 224 in1180:=integrate(z^(1/3)/(z^2+1), z= 0..10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) --R --R ---R (33) potentialPole +--R (24) potentialPole --R Type: Union(pole: potentialPole,...) ---E 34 +--E 24 ---S 35 of 267 +--S 25 of 224 in1180:=integrate(z^(1/3)/(z^2+1), z= 0..10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,"noPole") --R --R ---R (34) +--R (25) --R 3 --R * --R log @@ -637,75 +491,75 @@ in1180:=integrate(z^(1/3)/(z^2+1), z= 0..100000000000000000000000000000000000000 --R / --R 24 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 35 +--E 25 ---S 36 of 267 -in1183a:=integrate(csc(z), z= 1-I..1+I,"noPole") +--S 26 of 224 +in1183a:=integrate(csc(z), z= 1-%i..1+%i,"noPole") --R --R ---R (35) ---R 2 2 ---R sin(I + 1) sin(I - 1) ---R log(-----------------------------) - log(-----------------------------) ---R 2 2 ---R cos(I + 1) + 2cos(I + 1) + 1 cos(I - 1) + 2cos(I - 1) + 1 ---R ----------------------------------------------------------------------- ---R 2 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 36 +--R (26) +--R 2 2 +--R sin(1 + %i) sin(1 - %i) +--R log(-------------------------------) - log(-------------------------------) +--R 2 2 +--R cos(1 + %i) + 2cos(1 + %i) + 1 cos(1 - %i) + 2cos(1 - %i) + 1 +--R --------------------------------------------------------------------------- +--R 2 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 26 ---S 37 of 267 +--S 27 of 224 in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R --R ---R (36) +--R (27) --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 - 4\|2 %%BQ1 --R + --R +-+ ---I - 4\|2 %%BC0 +--I - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R * --R log --R +-+ +-+ +-+ +-+ ---I ((24576\|2 %%BC0 - 768\|2 )%%BC1 - 768\|2 %%BC0 - 48\|2 ) +--I ((24576\|2 %%BQ0 - 768\|2 )%%BQ1 - 768\|2 %%BQ0 - 48\|2 ) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R 2 2 ---I (196608%%BC0 - 6144)%%BC1 + (196608%%BC0 + 384)%%BC1 +--I (196608%%BQ0 - 6144)%%BQ1 + (196608%%BQ0 + 384)%%BQ1 --R + --R 2 ---I - 6144%%BC0 + 384%%BC0 + 48 +--I - 6144%%BQ0 + 384%%BQ0 + 48 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ ---I - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BQ1 - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R + ---I ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) +--I ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 +-+ ---I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 +--I (- 12288\|2 %%BQ0 + 48\|2 )%%BQ1 + 1536\|2 %%BQ0 + 48\|2 %%BQ0 --R + --R +-+ --R 60\|2 @@ -717,55 +571,55 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 - 4\|2 %%BQ1 --R + --R +-+ ---I - 4\|2 %%BC0 +--I - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R * --R log ---I ((24576%%BC0 - 768)%%BC1 - 768%%BC0 - 48) +--I ((24576%%BQ0 - 768)%%BQ1 - 768%%BQ0 - 48) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (98304\|2 %%BC0 - 3072\|2 )%%BC1 +--I (98304\|2 %%BQ0 - 3072\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 ---I (98304\|2 %%BC0 + 192\|2 )%%BC1 - 3072\|2 %%BC0 +--I (98304\|2 %%BQ0 + 192\|2 )%%BQ1 - 3072\|2 %%BQ0 --R + --R +-+ +-+ ---I 192\|2 %%BC0 + 24\|2 +--I 192\|2 %%BQ0 + 24\|2 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ ---I - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BQ1 - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R + ---I ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) +--I ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 +--I (- 12288\|2 %%BQ0 + 48\|2 )%%BQ1 + 1536\|2 %%BQ0 --R + --R +-+ +-+ ---I 48\|2 %%BC0 + 42\|2 +--I 48\|2 %%BQ0 + 42\|2 --R / --R +-+ --R \|2 @@ -774,56 +628,56 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I - \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 - 4\|2 %%BQ1 --R + --R +-+ ---I - 4\|2 %%BC0 +--I - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R * --R log --R +-+ +-+ +-+ ---I (24576\|2 %%BC0 - 768\|2 )%%BC1 - 768\|2 %%BC0 +--I (24576\|2 %%BQ0 - 768\|2 )%%BQ1 - 768\|2 %%BQ0 --R + --R +-+ --R - 48\|2 --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R 2 ---I (- 196608%%BC0 + 6144)%%BC1 +--I (- 196608%%BQ0 + 6144)%%BQ1 --R + --R 2 2 ---I (- 196608%%BC0 - 384)%%BC1 + 6144%%BC0 - 384%%BC0 - 48 +--I (- 196608%%BQ0 - 384)%%BQ1 + 6144%%BQ0 - 384%%BQ0 - 48 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I - \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ ---I - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BQ1 - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R + ---I ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) +--I ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 +--I (- 12288\|2 %%BQ0 + 48\|2 )%%BQ1 + 1536\|2 %%BQ0 --R + --R +-+ +-+ ---I 48\|2 %%BC0 + 60\|2 +--I 48\|2 %%BQ0 + 60\|2 --R / --R +-+ --R \|2 @@ -831,52 +685,52 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I - \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 - 4\|2 %%BQ1 --R + --R +-+ ---I - 4\|2 %%BC0 +--I - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R * --R log ---I ((24576%%BC0 - 768)%%BC1 - 768%%BC0 - 48) +--I ((24576%%BQ0 - 768)%%BQ1 - 768%%BQ0 - 48) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (- 98304\|2 %%BC0 + 3072\|2 )%%BC1 +--I (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 ---I (- 98304\|2 %%BC0 - 192\|2 )%%BC1 + 3072\|2 %%BC0 +--I (- 98304\|2 %%BQ0 - 192\|2 )%%BQ1 + 3072\|2 %%BQ0 --R + --R +-+ +-+ ---I - 192\|2 %%BC0 - 24\|2 +--I - 192\|2 %%BQ0 - 24\|2 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I - \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ ---I - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BQ1 - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R + ---I ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) +--I ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 +-+ ---I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 +--I (- 12288\|2 %%BQ0 + 48\|2 )%%BQ1 + 1536\|2 %%BQ0 + 48\|2 %%BQ0 --R + --R +-+ --R 42\|2 @@ -888,55 +742,55 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I - \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 - 4\|2 %%BQ1 --R + --R +-+ ---I - 4\|2 %%BC0 +--I - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R * --R log ---I ((- 24576%%BC0 + 768)%%BC1 + 768%%BC0 + 48) +--I ((- 24576%%BQ0 + 768)%%BQ1 + 768%%BQ0 + 48) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (98304\|2 %%BC0 - 3072\|2 )%%BC1 +--I (98304\|2 %%BQ0 - 3072\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 ---I (98304\|2 %%BC0 + 192\|2 )%%BC1 - 3072\|2 %%BC0 +--I (98304\|2 %%BQ0 + 192\|2 )%%BQ1 - 3072\|2 %%BQ0 --R + --R +-+ +-+ ---I 192\|2 %%BC0 + 24\|2 +--I 192\|2 %%BQ0 + 24\|2 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I - \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ ---I - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BQ1 - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R + ---I ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) +--I ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 +--I (- 12288\|2 %%BQ0 + 48\|2 )%%BQ1 + 1536\|2 %%BQ0 --R + --R +-+ +-+ ---I 48\|2 %%BC0 + 42\|2 +--I 48\|2 %%BQ0 + 42\|2 --R / --R +-+ --R \|2 @@ -944,53 +798,53 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I - \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 - 4\|2 %%BQ1 --R + --R +-+ ---I - 4\|2 %%BC0 +--I - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R * --R log --R +-+ +-+ +-+ ---I (- 24576\|2 %%BC0 + 768\|2 )%%BC1 + 768\|2 %%BC0 +--I (- 24576\|2 %%BQ0 + 768\|2 )%%BQ1 + 768\|2 %%BQ0 --R + --R +-+ --R 48\|2 --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R 2 2 ---I (196608%%BC0 - 6144)%%BC1 + (196608%%BC0 + 384)%%BC1 +--I (196608%%BQ0 - 6144)%%BQ1 + (196608%%BQ0 + 384)%%BQ1 --R + --R 2 ---I - 6144%%BC0 + 384%%BC0 + 48 +--I - 6144%%BQ0 + 384%%BQ0 + 48 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---I - \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I - \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ ---I - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BQ1 - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R + ---I ((3072%%BC0 - 384)%%BC1 - 384%%BC0 + 12) +--I ((3072%%BQ0 - 384)%%BQ1 - 384%%BQ0 + 12) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 +-+ ---I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 +--I (- 12288\|2 %%BQ0 + 48\|2 )%%BQ1 + 1536\|2 %%BQ0 + 48\|2 %%BQ0 --R + --R +-+ --R 60\|2 @@ -1001,52 +855,52 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 - 4\|2 %%BQ1 --R + --R +-+ ---I - 4\|2 %%BC0 +--I - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R * --R log ---I ((- 24576%%BC0 + 768)%%BC1 + 768%%BC0 + 48) +--I ((- 24576%%BQ0 + 768)%%BQ1 + 768%%BQ0 + 48) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (- 98304\|2 %%BC0 + 3072\|2 )%%BC1 +--I (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 ---I (- 98304\|2 %%BC0 - 192\|2 )%%BC1 + 3072\|2 %%BC0 +--I (- 98304\|2 %%BQ0 - 192\|2 )%%BQ1 + 3072\|2 %%BQ0 --R + --R +-+ +-+ ---I - 192\|2 %%BC0 - 24\|2 +--I - 192\|2 %%BQ0 - 24\|2 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ ---I - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BQ1 - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R + ---I ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) +--I ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 +-+ ---I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 + 48\|2 %%BC0 +--I (- 12288\|2 %%BQ0 + 48\|2 )%%BQ1 + 1536\|2 %%BQ0 + 48\|2 %%BQ0 --R + --R +-+ --R 42\|2 @@ -1058,199 +912,199 @@ in1185a:=integrate((z+1)^(1/2)/(1+z^4), z= 0..1,"noPole") --R ROOT --R +-----------------------------------------+ --R | 2 2 +-+ ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 - 4\|2 %%BC1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 - 4\|2 %%BQ1 --R + --R +-+ ---I - 4\|2 %%BC0 +--I - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R * --R log --R +-+ +-+ +-+ ---I (- 24576\|2 %%BC0 + 768\|2 )%%BC1 + 768\|2 %%BC0 +--I (- 24576\|2 %%BQ0 + 768\|2 )%%BQ1 + 768\|2 %%BQ0 --R + --R +-+ --R 48\|2 --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R 2 ---I (- 196608%%BC0 + 6144)%%BC1 +--I (- 196608%%BQ0 + 6144)%%BQ1 --R + --R 2 2 ---I (- 196608%%BC0 - 384)%%BC1 + 6144%%BC0 - 384%%BC0 - 48 +--I (- 196608%%BQ0 - 384)%%BQ1 + 6144%%BQ0 - 384%%BQ0 - 48 --R * --R ROOT --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ ---I - 4\|2 %%BC1 - 4\|2 %%BC0 +--I - 4\|2 %%BQ1 - 4\|2 %%BQ0 --R / --R +-+ --R 2\|2 --R + ---I ((- 3072%%BC0 + 384)%%BC1 + 384%%BC0 - 12) +--I ((- 3072%%BQ0 + 384)%%BQ1 + 384%%BQ0 - 12) --R * --R +-----------------------------------------+ --R | 2 2 ---I \|- 96%%BC1 - 64%%BC0 %%BC1 - 96%%BC0 - 1 +--I \|- 96%%BQ1 - 64%%BQ0 %%BQ1 - 96%%BQ0 - 1 --R + --R +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 1536\|2 )%%BC1 +--I (- 12288\|2 %%BQ0 + 1536\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 2 ---I (- 12288\|2 %%BC0 + 48\|2 )%%BC1 + 1536\|2 %%BC0 +--I (- 12288\|2 %%BQ0 + 48\|2 )%%BQ1 + 1536\|2 %%BQ0 --R + --R +-+ +-+ ---I 48\|2 %%BC0 + 60\|2 +--I 48\|2 %%BQ0 + 60\|2 --R / --R +-+ --R \|2 --R + --R - --R +------+ ---I \|4%%BC1 +--I \|4%%BQ1 --R * --R log --R +-+ +-+ 2 ---I (98304\|2 %%BC0 - 3072\|2 )%%BC1 +--I (98304\|2 %%BQ0 - 3072\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 3 ---I (98304\|2 %%BC0 + 192\|2 )%%BC1 + 98304\|2 %%BC0 +--I (98304\|2 %%BQ0 + 192\|2 )%%BQ1 + 98304\|2 %%BQ0 --R + --R +-+ +-+ ---I 768\|2 %%BC0 - 36\|2 +--I 768\|2 %%BQ0 - 36\|2 --R * --R +------+ ---I \|4%%BC1 +--I \|4%%BQ1 --R + --R 2 2 ---I (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 +--I (12288%%BQ0 - 1536)%%BQ1 + (12288%%BQ0 - 48)%%BQ1 --R + --R 3 ---I 12288%%BC0 + 96%%BC0 + 18 +--I 12288%%BQ0 + 96%%BQ0 + 18 --R + --R +------+ ---I \|4%%BC1 +--I \|4%%BQ1 --R * --R log --R 2 2 ---I (98304%%BC0 - 3072)%%BC1 + (98304%%BC0 + 192)%%BC1 +--I (98304%%BQ0 - 3072)%%BQ1 + (98304%%BQ0 + 192)%%BQ1 --R + --R 3 ---I 98304%%BC0 + 768%%BC0 - 36 +--I 98304%%BQ0 + 768%%BQ0 - 36 --R * --R +------+ ---I \|4%%BC1 +--I \|4%%BQ1 --R + --R 2 2 3 ---I (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 + 12288%%BC0 +--I (12288%%BQ0 - 1536)%%BQ1 + (12288%%BQ0 - 48)%%BQ1 + 12288%%BQ0 --R + ---I 96%%BC0 + 9 +--I 96%%BQ0 + 9 --R + --R - --R +------+ ---I \|4%%BC1 +--I \|4%%BQ1 --R * --R log --R 2 2 ---I (- 98304%%BC0 + 3072)%%BC1 + (- 98304%%BC0 - 192)%%BC1 +--I (- 98304%%BQ0 + 3072)%%BQ1 + (- 98304%%BQ0 - 192)%%BQ1 --R + --R 3 ---I - 98304%%BC0 - 768%%BC0 + 36 +--I - 98304%%BQ0 - 768%%BQ0 + 36 --R * --R +------+ ---I \|4%%BC1 +--I \|4%%BQ1 --R + --R 2 2 ---I (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 +--I (12288%%BQ0 - 1536)%%BQ1 + (12288%%BQ0 - 48)%%BQ1 --R + --R 3 ---I 12288%%BC0 + 96%%BC0 + 9 +--I 12288%%BQ0 + 96%%BQ0 + 9 --R + --R +------+ ---I \|4%%BC1 +--I \|4%%BQ1 --R * --R log --R +-+ +-+ 2 ---I (- 98304\|2 %%BC0 + 3072\|2 )%%BC1 +--I (- 98304\|2 %%BQ0 + 3072\|2 )%%BQ1 --R + --R +-+ 2 +-+ +-+ 3 ---I (- 98304\|2 %%BC0 - 192\|2 )%%BC1 - 98304\|2 %%BC0 +--I (- 98304\|2 %%BQ0 - 192\|2 )%%BQ1 - 98304\|2 %%BQ0 --R + --R +-+ +-+ ---I - 768\|2 %%BC0 + 36\|2 +--I - 768\|2 %%BQ0 + 36\|2 --R * --R +------+ ---I \|4%%BC1 +--I \|4%%BQ1 --R + --R 2 2 3 ---I (12288%%BC0 - 1536)%%BC1 + (12288%%BC0 - 48)%%BC1 + 12288%%BC0 +--I (12288%%BQ0 - 1536)%%BQ1 + (12288%%BQ0 - 48)%%BQ1 + 12288%%BQ0 --R + ---I 96%%BC0 + 18 +--I 96%%BQ0 + 18 --R + --R +------+ ---I \|4%%BC0 +--I \|4%%BQ0 --R * --R log --R +-+ 3 +-+ 2 +-+ +-+ ---I (98304\|2 %%BC0 + 3072\|2 %%BC0 + 576\|2 %%BC0 - 60\|2 ) +--I (98304\|2 %%BQ0 + 3072\|2 %%BQ0 + 576\|2 %%BQ0 - 60\|2 ) --R * --R +------+ ---I \|4%%BC0 +--I \|4%%BQ0 --R + --R 3 2 ---I - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 30 +--I - 12288%%BQ0 - 1536%%BQ0 - 144%%BQ0 + 30 --R + --R - --R +------+ ---I \|4%%BC0 +--I \|4%%BQ0 --R * --R log --R 3 2 +------+ ---I (98304%%BC0 + 3072%%BC0 + 576%%BC0 - 60)\|4%%BC0 +--I (98304%%BQ0 + 3072%%BQ0 + 576%%BQ0 - 60)\|4%%BQ0 --R + --R 3 2 ---I - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 21 +--I - 12288%%BQ0 - 1536%%BQ0 - 144%%BQ0 + 21 --R + --R +------+ ---I \|4%%BC0 +--I \|4%%BQ0 --R * --R log --R 3 2 +------+ ---I (- 98304%%BC0 - 3072%%BC0 - 576%%BC0 + 60)\|4%%BC0 +--I (- 98304%%BQ0 - 3072%%BQ0 - 576%%BQ0 + 60)\|4%%BQ0 --R + --R 3 2 ---I - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 21 +--I - 12288%%BQ0 - 1536%%BQ0 - 144%%BQ0 + 21 --R + --R - --R +------+ ---I \|4%%BC0 +--I \|4%%BQ0 --R * --R log --R +-+ 3 +-+ 2 +-+ +-+ ---I (- 98304\|2 %%BC0 - 3072\|2 %%BC0 - 576\|2 %%BC0 + 60\|2 ) +--I (- 98304\|2 %%BQ0 - 3072\|2 %%BQ0 - 576\|2 %%BQ0 + 60\|2 ) --R * --R +------+ ---I \|4%%BC0 +--I \|4%%BQ0 --R + --R 3 2 ---I - 12288%%BC0 - 1536%%BC0 - 144%%BC0 + 30 +--I - 12288%%BQ0 - 1536%%BQ0 - 144%%BQ0 + 30 --R / --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 37 +--E 27 ---S 38 of 267 +--S 28 of 224 in1186a:=integrate((z^2+z)^(1/2)/(1+z^2)^2, z= 0..1,"noPole") --R --R ---R (37) +--R (28) --R +-+ 4+-+ %pi --R (17\|2 - 24)\|2 cos(---) --R 8 @@ -1416,13 +1270,13 @@ in1186a:=integrate((z^2+z)^(1/2)/(1+z^2)^2, z= 0..1,"noPole") --R +-+ --R 384\|2 - 544 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 38 +--E 28 ---S 39 of 267 +--S 29 of 224 in1190a:=integrate(sin(z)^2*tan(z)^(1/2), z= 0..1,"noPole") --R --R ---R (38) +--R (29) --R +------+ --R 3 4 2 |sin(1) --R ((96cos(1) + 24cos(1))sin(1) - 96cos(1) + 120cos(1) ) |------ @@ -1566,13 +1420,13 @@ in1190a:=integrate(sin(z)^2*tan(z)^(1/2), z= 0..1,"noPole") --R 4 2 --R - 1024cos(1)sin(1) + 2048cos(1) - 2048cos(1) - 64 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 39 +--E 29 ---S 40 of 267 +--S 30 of 224 in1191a:=integrate(sin(z)^2/tan(z)^(1/2), z= 0..1,"noPole") --R --R ---R (39) +--R (30) --R +------+ --R 3 4 2 |sin(1) --R ((- 32cos(1) - 8cos(1))sin(1) + 32cos(1) - 40cos(1) ) |------ @@ -1711,29 +1565,29 @@ in1191a:=integrate(sin(z)^2/tan(z)^(1/2), z= 0..1,"noPole") --R 4 2 --R - 1024cos(1)sin(1) + 2048cos(1) - 2048cos(1) - 64 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 40 +--E 30 ---S 41 of 267 +--S 31 of 224 in1193a:=integrate(-sin(z)^2*cot(z-1), z= 0..1,"noPole") --R --R ---R (40) + infinity +--R (31) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 41 +--E 31 ---S 42 of 267 +--S 32 of 224 in1207:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1) --R --R ---R (41) potentialPole +--R (32) potentialPole --R Type: Union(pole: potentialPole,...) ---E 42 +--E 32 ---S 43 of 267 +--S 33 of 224 in1207a:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1,"noPole") --R --R ---R (42) +--R (33) --R +------+ --R 3 4 2 |sin(1) --R ((- 32cos(1) - 8cos(1))sin(1) + 32cos(1) - 40cos(1) ) |------ @@ -1872,21 +1726,21 @@ in1207a:=integrate(sin(z)*cos(z)*tan(z)^(1/2), z= 0..1,"noPole") --R 4 2 --R - 1024cos(1)sin(1) + 2048cos(1) - 2048cos(1) - 64 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 43 +--E 33 ---S 44 of 267 +--S 34 of 224 in1210a:=integrate(-sin(z)*cos(z)*cot(z-1), z= 0..1,"noPole") --R --R ---R (43) + infinity +--R (34) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 44 +--E 34 ---S 45 of 267 +--S 35 of 224 in1214a:=integrate(-sin(z)*tan(z)*csc(z-1), z= 0..1,"noPole") --R --R ---R (44) +--R (35) --R 1 2 1 2 --R 4cos(-) sin(-) --R 2 2 @@ -1935,13 +1789,13 @@ in1214a:=integrate(-sin(z)*tan(z)*csc(z-1), z= 0..1,"noPole") --R 2sin(-) - 2cos(-) --R 2 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 45 +--E 35 ---S 46 of 267 +--S 36 of 224 in1217a:=integrate(sin(z)*sec(z)*tan(z)^(1/2), z= 0..1,"noPole") --R --R ---R (45) +--R (36) --R +------+ --R |sin(1) +-+ --R (2cos(1) |------ + (- sin(1) - cos(1))\|2 ) @@ -2039,13 +1893,13 @@ in1217a:=integrate(sin(z)*sec(z)*tan(z)^(1/2), z= 0..1,"noPole") --R 16cos(1)\|2 |------ - 16sin(1) - 16cos(1) --R \|cos(1) --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 46 +--E 36 ---S 47 of 267 +--S 37 of 224 in1218a:=integrate(sin(z)*sec(z)/tan(z)^(1/2), z= 0..1,"noPole") --R --R ---R (46) +--R (37) --R +-+ --R 2\|2 --R * @@ -2100,32 +1954,21 @@ in1218a:=integrate(sin(z)*sec(z)/tan(z)^(1/2), z= 0..1,"noPole") --R / --R 16 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 47 +--E 37 ---S 48 of 267 +--S 38 of 224 in1a:=integrate(log(abs(z^2-1))/(1+z)^2, z= 0..%plusInfinity,"noPole") --R --R ---R (47) 1 +--R (38) 1 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 48 - ---S 49 of 267 -in13:=integrate(cos(z)^2*sin(z)^n, z) ---R ---R ---R z ---R ++ 2 n ---I (48) | cos(%K) sin(%K) d%K ---R ++ ---R Type: Union(Expression Integer,...) ---E 49 +--E 38 ---S 50 of 267 +--S 39 of 224 in15ab:=integrate(log(sqrt(z)+z^5), z=0..a,"noPole") --R --R ---R (49) +--R (39) --R %pi --R 6cos(---) --R 9 @@ -2295,66 +2138,58 @@ in15ab:=integrate(log(sqrt(z)+z^5), z=0..a,"noPole") --R / --R 12 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 50 +--E 39 ---S 51 of 267 +--S 40 of 224 in20a:=integrate(log(sin(z)^2+cos(z)^2), z= 0..1,"noPole") --R --R ---R (50) 0 +--R (40) 0 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 51 +--E 40 ---S 52 of 267 +--S 41 of 224 in126a:=integrate(atan(1/cot(z)), z= 0..2*%pi,"noPole") --R --R --R 2 ---R (51) 2%pi +--R (41) 2%pi --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 52 +--E 41 ---S 53 of 267 +--S 42 of 224 in128a:=integrate(atan(sqrt(1-cos(z)^2)/(1+cos(z))), z= 0..1,"noPole") --R --R --R 1 ---R (52) - +--R (42) - --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 53 - ---S 54 of 267 -in134:=integrate(log(exp(z)), z= -I..I) ---R ---R ---R (53) 0 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 54 +--E 42 ---S 55 of 267 +--S 43 of 224 in134a:=integrate(log(exp(z)), z= -%i..%i) --R --R ---R (54) 0 +--R (43) 0 --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 55 +--E 43 ---S 56 of 267 +--S 44 of 224 in1221a:=integrate(sin(z)*csc(z)*acoth(1/z), z= 0..1,"noPole") --R --R --R log(4) ---R (55) ------ +--R (44) ------ --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 56 +--E 44 ---S 57 of 267 +--S 45 of 224 in1228a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole") --R --R ---R (56) +--R (45) --R +-+ --R 2\|2 --R * @@ -2409,23 +2244,23 @@ in1228a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole") --R / --R 16 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 57 +--E 45 ---S 58 of 267 +--S 46 of 224 in1241a:=integrate(sin(z)*csc(z)*acoth(1/z), z= 0..1,"noPole") --R --R --R log(4) ---R (57) ------ +--R (46) ------ --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 58 +--E 46 ---S 59 of 267 +--S 47 of 224 in1248a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole") --R --R ---R (58) +--R (47) --R +-+ --R 2\|2 --R * @@ -2480,13 +2315,13 @@ in1248a:=integrate(sin(z)*csc(z)*tan(z)^(1/2), z= 0..1,"noPole") --R / --R 16 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 59 +--E 47 ---S 60 of 267 +--S 48 of 224 in1261a:=integrate(1/(sin(z)+cos(2*z)), z= -1..1,"noPole") --R --R ---R (59) +--R (48) --R 2 2 --R (- sin(1) + cos(1) + 2cos(1) + 1) --R * @@ -2529,119 +2364,111 @@ in1261a:=integrate(1/(sin(z)+cos(2*z)), z= -1..1,"noPole") --R 2 2 +-+ --R (3sin(1) - 3cos(1) - 6cos(1) - 3)\|3 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 60 - ---S 61 of 267 -in1273a:=integrate((1/(z-I))^(1/2), z= 0..%plusInfinity,"noPole") ---R ---R ---R (60) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 61 +--E 48 ---S 62 of 267 -in1274a:=integrate(1/(1/(z-I))^(1/2), z= 0..%plusInfinity,"noPole") +--S 49 of 224 +in1273a:=integrate((1/(z-%i))^(1/2), z= 0..%plusInfinity,"noPole") --R --R ---R (61) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 62 +--R (49) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 49 ---S 63 of 267 -in1278a:=integrate((1+1/(I*z)^(1/2))^(1/2), z= 0..%plusInfinity,"noPole") +--S 50 of 224 +in1274a:=integrate(1/(1/(z-%i))^(1/2), z= 0..%plusInfinity,"noPole") --R --R ---R (62) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 63 +--R (50) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 50 ---S 64 of 267 +--S 51 of 224 in1284a:=integrate(log(1+2^(1/2)/z^(1/4)-1/z^(1/2)), z= 0..%plusInfinity,"noPole") --R --R ---R (63) + infinity +--R (51) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 64 +--E 51 ---S 65 of 267 +--S 52 of 224 in1314a:=integrate(log(1-z)*atanh(z^(1/2)), z= 0..1,"noPole") --R --R --R log(16) - 6 ---R (64) ----------- +--R (52) ----------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 65 +--E 52 ---S 66 of 267 -in1359a:=integrate((I*z)^(1/2)*(-I*z)^(1/2), z= %minusInfinity..%plusInfinity,"noPole") +--S 53 of 224 +in1359a:=integrate((%i*z)^(1/2)*(-%i*z)^(1/2), z= %minusInfinity..%plusInfinity,"noPole") --R --R ---R (65) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 66 +--R (53) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 53 ---S 67 of 267 +--S 54 of 224 in1376a:=integrate(z*acoth(z^(1/2)), z= 0..1,"noPole") --R --R --R 2 ---R (66) - +--R (54) - --R 3 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 67 +--E 54 ---S 68 of 267 +--S 55 of 224 in1377a:=integrate(z*acoth(1-z), z= 0..1,"noPole") --R --R --R log(4) - 1 ---R (67) ---------- +--R (55) ---------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 68 +--E 55 ---S 69 of 267 +--S 56 of 224 in1378a:=integrate(z*acoth(1-(1-z)^(1/2)), z= 0..1,"noPole") --R --R --R - 3log(4) + 5 ---R (68) ------------- +--R (56) ------------- --R 3 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 69 +--E 56 ---S 70 of 267 +--S 57 of 224 in1392a:=integrate(acoth(z^(1/2)), z= 0..1,"noPole") --R --R ---R (69) 1 +--R (57) 1 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 70 +--E 57 ---S 71 of 267 +--S 58 of 224 in1397a:=integrate(1/(-1+z^(1/2))^(1/2), z= 1..2,"noPole") --R --R --R +--------+ --R +-+ | +-+ --R (4\|2 + 8)\|\|2 - 1 ---R (70) ---------------------- +--R (58) ---------------------- --R 3 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 71 +--E 58 ---S 72 of 267 +--S 59 of 224 in1398a:=integrate(acoth(1/z), z= 1..2,"noPole") --R --R --R 3log(9) - 2log(4) ---R (71) ----------------- +--R (59) ----------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 72 +--E 59 ---S 73 of 267 +--S 60 of 224 in1399a:=integrate(acoth(1/z^(1/2)), z= 1..2,"noPole") --R --R @@ -2650,16 +2477,16 @@ in1399a:=integrate(acoth(1/z^(1/2)), z= 1..2,"noPole") --R log(-----------) + 4\|2 - 4 --R +-+ --R 2\|2 - 3 ---R (72) ---------------------------- +--R (60) ---------------------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 73 +--E 60 ---S 74 of 267 +--S 61 of 224 in143a:=integrate(sqrt(1+z)/(1+z^2), z= 0..1,"noPole") --R --R ---R (73) +--R (61) --R 4+-+ %pi --R \|2 cos(---) --R 8 @@ -2758,928 +2585,1256 @@ in143a:=integrate(sqrt(1+z)/(1+z^2), z= 0..1,"noPole") --R / --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 74 +--E 61 ---S 75 of 267 -in144:=integrate(1, z= I*infinity..%plusInfinity) +--S 62 of 224 +in144:=integrate(1, z= %i*infinity..%plusInfinity) --R --R ---R (74) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 75 +--R (62) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 62 ---S 76 of 267 -in146a:=integrate(csc(z), z= 1-I..1+I,"noPole") +--S 63 of 224 +in146a:=integrate(csc(z), z= 1-%i..1+%i,"noPole") --R --R ---R (75) ---R 2 2 ---R sin(I + 1) sin(I - 1) ---R log(-----------------------------) - log(-----------------------------) ---R 2 2 ---R cos(I + 1) + 2cos(I + 1) + 1 cos(I - 1) + 2cos(I - 1) + 1 ---R ----------------------------------------------------------------------- ---R 2 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 76 +--R (63) +--R 2 2 +--R sin(1 + %i) sin(1 - %i) +--R log(-------------------------------) - log(-------------------------------) +--R 2 2 +--R cos(1 + %i) + 2cos(1 + %i) + 1 cos(1 - %i) + 2cos(1 - %i) + 1 +--R --------------------------------------------------------------------------- +--R 2 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 63 ---S 77 of 267 +--S 64 of 224 in148:=integrate(min(1,z), z= 0..2) --R --R ---R (76) 2 +--R (64) 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 77 +--E 64 ---S 78 of 267 +--S 65 of 224 in156a:=integrate(z^(2/3), z= 1..10,"noPole") --R --R --R 3+--+2 --R 30\|10 - 3 ---R (77) ------------ +--R (65) ------------ --R 5 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 78 - ---S 79 of 267 -in159a:=integrate(log(z)/z^2, z= -I..-1,"noPole") ---R ---R ---R 2 ---R - log(I ) + 2I - 2 ---R (78) ------------------ ---R 2I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 79 - ---S 80 of 267 -in160:=integrate((-z^2-z)^sin(z), z) ---R ---R ---R z ---I ++ 2 sin(%K) ---I (79) | (- %K - %K) d%K ---R ++ ---R Type: Union(Expression Integer,...) ---E 80 - ---S 81 of 267 -in1425a:=integrate(-(z^2+I*z+3)/(z^2+I*z+2), z= 0..%plusInfinity,"noPole") ---R ---R ---R (80) [- infinity,- infinity] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 81 - ---S 82 of 267 -in1426a:=integrate(-I/(1+I*z^3)*z^3, z= 0..%plusInfinity,"noPole") ---R ---R ---R (81) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 82 - ---S 83 of 267 -in1428a:=integrate(-I/(1+I*z)*z, z= 0..%plusInfinity,"noPole") ---R ---R ---R (82) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 83 +--E 65 ---S 84 of 267 -in1432:=integrate(-(z+I)*(-1+1/(z+I)), z= 0..%plusInfinity) +--S 66 of 224 +in1425a:=integrate(-(z^2+%i*z+3)/(z^2+%i*z+2), z= 0..%plusInfinity,"noPole") --R --R ---R (83) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 84 +--R (66) - infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 66 ---S 85 of 267 -in1433a:=integrate(-1/((I*z)^(1/2)-1)*(-2+(I*z)^(1/2)), z= 0..%plusInfinity,"noPole") +--S 67 of 224 +in1426a:=integrate(-%i/(1+%i*z^3)*z^3, z= 0..%plusInfinity,"noPole") --R --R ---R (84) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 85 +--R (67) - infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 67 ---S 86 of 267 -in1434a:=integrate(-(1+(I*z)^(1/2))/(I*z)^(1/2), z= 0..%plusInfinity,"noPole") +--S 68 of 224 +in1428a:=integrate(-%i/(1+%i*z)*z, z= 0..%plusInfinity,"noPole") --R --R ---R (85) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 86 +--R (68) - infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 68 ---S 87 of 267 -in1435a:=integrate(-1/(1+(I*z)^(1/2))*(I*z)^(1/2), z= 0..%plusInfinity,"noPole") +--S 69 of 224 +in1432:=integrate(-(z+%i)*(-1+1/(z+%i)), z= 0..%plusInfinity) --R --R ---R (86) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 87 +--R (69) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 69 ---S 88 of 267 -in1436a:=integrate(-((I*z)^(1/2)-1)/(-2+(I*z)^(1/2)), z= 0..%plusInfinity,"noPole") +--S 70 of 224 +in1434a:=integrate(-(1+(%i*z)^(1/2))/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole") --R --R ---R (87) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 88 +--R (70) - infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 70 ---S 89 of 267 -in1440a:=integrate((1-(I*z)^(1/2))/(I*z)^(1/2), z= 0..%plusInfinity,"noPole") +--S 71 of 224 +in1440a:=integrate((1-(%i*z)^(1/2))/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole") --R --R ---R (88) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 89 +--R (71) - infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 71 ---S 90 of 267 -in1460:=integrate(z^2+I*z+3, z= 0..%plusInfinity) +--S 72 of 224 +in1460:=integrate(z^2+%i*z+3, z= 0..%plusInfinity) --R --R ---R (89) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 90 +--R (72) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 72 ---S 91 of 267 -in1463a:=integrate(1-(I*z)^(1/2)/(1-I*z), z= 0..%plusInfinity,"noPole") +--S 73 of 224 +in1464a:=integrate(1+1/(%i*z)^(1/2), z= 0..%plusInfinity,"noPole") --R --R ---R (90) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 91 +--R (73) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 73 ---S 92 of 267 -in1464a:=integrate(1+1/(I*z)^(1/2), z= 0..%plusInfinity,"noPole") +--S 74 of 224 +in2045:=integrate(atan(1/tan(z)), z= 0..2*%pi,"noPole") --R --R ---R (91) + infinity +--R 2 +--R (74) - 3%pi --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 92 - ---S 93 of 267 used to work -in2045:=integrate(atan(1/tan(z)), z= 0..2*Pi) ---R ---R There are 34 exposed and 23 unexposed library operations named * ---R having 2 argument(s) but none was determined to be applicable. ---R Use HyperDoc Browse, or issue ---R )display op * ---R to learn more about the available operations. Perhaps ---R package-calling the operation or using coercions on the arguments ---R will allow you to apply the operation. ---R ---RDaly Bug ---R Cannot find a definition or applicable library operation named * ---R with argument type(s) ---R PositiveInteger ---R Domain ---R ---R Perhaps you should use "@" to indicate the required return type, ---R or "$" to specify which version of the function you need. ---E 93 --- --- 2 --- - 3%pi --- Type: Union(f1: OrderedCompletion Expression Integer,...) +--E 74 ---S 94 of 267 +--S 75 of 224 in1502a:=integrate(log(z)^2*log(-z), z= 0..%plusInfinity,"noPole") --R --R ---R (92) + infinity +--R (75) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 94 - ---S 94 of 267 -in1512a:=integrate(log(z)*(1/(z-I))^(1/2), z= 1..%plusInfinity,"noPole") ---R ---R ---R (93) [ + infinity, + infinity] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 94 +--E 75 ---S 96 of 267 -in1513a:=integrate(log(z)*(1/(z+I))^(1/2), z= 1..%plusInfinity,"noPole") +--S 76 of 224 +in1512a:=integrate(log(z)*(1/(z-%i))^(1/2), z= 1..%plusInfinity,"noPole") --R --R ---R (94) [ + infinity, + infinity] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 96 +--R (76) [ + infinity, + infinity] +--R Type: Union(f2: List OrderedCompletion Expression Complex Integer,...) +--E 76 ---S 97 of 267 -in1514a:=integrate(log(z)/(I/(z-I))^(1/2), z= 1..%plusInfinity,"noPole") +--S 77 of 224 +in1513a:=integrate(log(z)*(1/(z+%i))^(1/2), z= 1..%plusInfinity,"noPole") --R --R ---R (95) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 97 +--R (77) [ + infinity, + infinity] +--R Type: Union(f2: List OrderedCompletion Expression Complex Integer,...) +--E 77 ---S 98 of 267 -in1563a:=integrate(log(1-z^3)*(I*z)^(1/2), z= 0..1,"noPole") +--S 78 of 224 +in1514a:=integrate(log(z)/(%i/(z-%i))^(1/2), z= 1..%plusInfinity,"noPole") --R --R ---R 2 ---R 16I 2 +-+ ---R (log(----) - log(I ) + log(9) - 4)\|I ---R 9 ---R (96) [--------------------------------------,- infinity] ---R 3 ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 98 +--R (78) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 78 ---S 99 of 267 +--S 79 of 224 in161:=integrate((-z^2)^(1/3), z) --R --R --R +----+ --R 3| 2 --R 3z\|- z ---R (97) --------- +--R (79) --------- --R 5 --R Type: Union(Expression Integer,...) ---E 99 - ---S 100 of 267 -in163:=integrate(log(z)*abs(exp(z)/z), z) ---R ---R ---I z %K ---R ++ %e ---I (98) | log(%K)abs(----)d%K ---I ++ %K ---R Type: Union(Expression Integer,...) ---E 100 - ---S 101 of 267 -in166:=integrate((1+z)^z, z) ---R ---R ---R z ---I ++ %K ---I (99) | (%K + 1) d%K ---R ++ ---R Type: Union(Expression Integer,...) ---E 101 +--E 79 ---S 102 of 267 +--S 80 of 224 in179:=integrate(1/(1+(3*z+1)^2), z) --R --R ---R atan(3z + 1) ---R (100) ------------ ---R 3 +--R atan(3z + 1) +--R (80) ------------ +--R 3 --R Type: Union(Expression Integer,...) ---E 102 +--E 80 ---S 103 of 267 -in1636a:=integrate(-z/(z-1)/(1/(z-I))^(1/2), z= 0..1,"noPole") +--S 81 of 224 +in1636a:=integrate(-z/(z-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole") --R --R ---R (101) +--R (81) --R [ + infinity, --R ---R +-------+ +---+ ---R +-----+ \|- I + 1 +-----+ \|- I ---R 6\|I - 1 log(- ----------) - 6\|I - 1 atan(--------) ---R +-----+ +-----+ ---R 2\|I - 1 \|I - 1 +--R +------+ +----+ +--R +---------+ \|1 - %i +---------+ 2\|- %i +--R 3\|- 4 + 4%i log(- ------------) - 3\|- 4 + 4%i atan(------------) +--R +---------+ +---------+ +--R \|- 4 + 4%i \|- 4 + 4%i --R + ---R +-------+ +---+ ---R (2I - 8)\|- I + 1 + (- 2I + 6)\|- I +--R +------+ +----+ +--R (- 8 + 2%i)\|1 - %i + (6 - 2%i)\|- %i --R / --R 3 --R ] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 103 - ---S 104 of 267 -in1638a:=integrate(-z/(z-1)/(1-I*z)^(1/2), z= 0..1,"noPole") ---R ---R ---R (102) ---R [ + infinity, ---R ---R +-------+ +-----+ +-----+ ---R \|- I + 1 \|I - 1 \|I - 1 ---R - 2I log(- ------------------) + 2I atan(--------) ---R 2I - 2 I - 1 ---R + ---R +-------+ +-----+ ---R (2\|- I + 1 - 2)\|I - 1 ---R / ---R +-----+ ---R I\|I - 1 ---R ] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 104 +--R Type: Union(f2: List OrderedCompletion Expression Complex Integer,...) +--E 81 ---S 105 of 267 -in1639a:=integrate(-z/(z-1)/(1-I*z^2)^(1/2), z= 0..1,"noPole") +--S 82 of 224 +in1639a:=integrate(-z/(z-1)/(1-%i*z^2)^(1/2), z= 0..1,"noPole") --R --R ---R (103) ---R [ + infinity, ---R ---R +-----+ ---R \|I - 1 ---R * ---R log ---R 2 +---+ 2 +-------+ 2 +---+ ---R ((2I - 4I)\|- I + 4I - 2I)\|- I + 1 + (- 4I + 4I)\|- I ---R + ---R 3 2 ---R 2I - 5I + 2I ---R / ---R +-------+ ---R 2\|- I + 1 + I - 2 ---R + ---R +-------+ +-----+ +-----+ ---R +---+ (- \|- I + 1 - I + 1)\|I - 1 +---+ \|I - 1 ---R 4\|- I log(------------------------------) + 4\|- I atan(--------) ---R +-------+ I - 1 ---R (2I - 2)\|- I + 1 - 2I + 2 ---R + ---R +-----+ ---R - log(- I)\|I - 1 ---R / ---R +---+ +-----+ ---R 2\|- I \|I - 1 ---R , ---R + infinity, ---R ---R +-------+ +-----+ ---R +-+ (- \|- I + 1 - I + 1)\|I - 1 ---R 2\|I log(------------------------------) ---R +-------+ ---R (2I - 2)\|- I + 1 - 2I + 2 ---R + ---R +-------+ +-+ +-----+ ---R +-----+ (\|- I + 1 - 1)\|I +-+ \|I - 1 ---R 2\|I - 1 atan(--------------------) + 2\|I atan(--------) ---R I I - 1 ---R / ---R +-----+ +-+ ---R \|I - 1 \|I ---R ] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 105 +--R (82) +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 + 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R * +--R log +--R +------+ +-+ +----+ +------+ +--R (16\|1 - %i - 16%i)\|2 + (48 - 16%i)\|- %i \|1 - %i +--R + +--R +----+ +--R (- 16 + 16%i)\|- %i +--R * +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 + 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R + +--R +------+ +-+ +----+ +------+ +--R (- 32\|1 - %i + 64 - 64%i)\|2 + (32 + 32%i)\|- %i \|1 - %i +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 + 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R * +--R log +--R +------------------------+ +--R | +-+ +----+ +--R +-+ +----+ |(1 + 3%i)\|2 + 2\|- %i +--R ((16 - 16%i)\|2 + 32\|- %i ) |------------------------ +--R | +-+ +--R \| \|2 +--R + +--R +-+ +----+ +--R (32 - 32%i)\|2 + (32 + 32%i)\|- %i +--R / +--R +-+ +--R \|2 +--R + +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 - 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R * +--R log +--R +------+ +-+ +----+ +------+ +--R (16\|1 - %i - 16%i)\|2 + (- 48 + 16%i)\|- %i \|1 - %i +--R + +--R +----+ +--R (16 - 16%i)\|- %i +--R * +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 - 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R + +--R +------+ +-+ +----+ +------+ +--R (- 32\|1 - %i + 64 - 64%i)\|2 + (- 32 - 32%i)\|- %i \|1 - %i +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 - 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R * +--R log +--R +------------------------+ +--R | +-+ +----+ +--R +-+ +----+ |(1 + 3%i)\|2 - 2\|- %i +--R ((16 - 16%i)\|2 - 32\|- %i ) |------------------------ +--R | +-+ +--R \| \|2 +--R + +--R +-+ +----+ +--R (32 - 32%i)\|2 + (- 32 - 32%i)\|- %i +--R / +--R +-+ +--R \|2 +--R + +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 - 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R * +--R log +--R +------------------------+ +--R | +-+ +----+ +--R +-+ +----+ |(1 + 3%i)\|2 - 2\|- %i +--R ((- 16 + 16%i)\|2 + 32\|- %i ) |------------------------ +--R | +-+ +--R \| \|2 +--R + +--R +-+ +----+ +--R (32 - 32%i)\|2 + (- 32 - 32%i)\|- %i +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 - 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R * +--R log +--R +------+ +-+ +----+ +------+ +--R (- 16\|1 - %i + 16%i)\|2 + (48 - 16%i)\|- %i \|1 - %i +--R + +--R +----+ +--R (- 16 + 16%i)\|- %i +--R * +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 - 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R + +--R +------+ +-+ +----+ +------+ +--R (- 32\|1 - %i + 64 - 64%i)\|2 + (- 32 - 32%i)\|- %i \|1 - %i +--R / +--R +-+ +--R \|2 +--R + +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 + 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R * +--R log +--R +------------------------+ +--R | +-+ +----+ +--R +-+ +----+ |(1 + 3%i)\|2 + 2\|- %i +--R ((- 16 + 16%i)\|2 - 32\|- %i ) |------------------------ +--R | +-+ +--R \| \|2 +--R + +--R +-+ +----+ +--R (32 - 32%i)\|2 + (32 + 32%i)\|- %i +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 + 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R * +--R log +--R +------+ +-+ +--R (- 16\|1 - %i + 16%i)\|2 +--R + +--R +----+ +------+ +----+ +--R (- 48 + 16%i)\|- %i \|1 - %i + (16 - 16%i)\|- %i +--R * +--R +------------------------+ +--R | +-+ +----+ +--R |(1 + 3%i)\|2 + 2\|- %i +--R |------------------------ +--R | +-+ +--R \| \|2 +--R + +--R +------+ +-+ +----+ +------+ +--R (- 32\|1 - %i + 64 - 64%i)\|2 + (32 + 32%i)\|- %i \|1 - %i +--R / +--R +-+ +--R \|2 +--R / +--R 4 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 82 ---S 106 of 267 -in1712a:=integrate(-log(-z)*(-I*z)^(1/2), z= 0..1,"noPole") +--S 83 of 224 +in1712a:=integrate(-log(-z)*(-%i*z)^(1/2), z= 0..1,"noPole") --R --R ---R +---+ ---R 4\|- I ---R (104) ------- +--R +----+ +--R 4\|- %i +--R (83) -------- --R 9 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 106 - ---S 107 of 267 -in1720a:=integrate(-z^2/(z^2-1)*(1/(z-I))^(1/2), z= 0..1,"noPole") ---R ---R ---R (105) ---R [ + infinity, ---R ---R +-----+ 2 +-------+ +---+ 3 2 ---R - \|I - 1 log((- 8I - 12I - 4)\|- I - 1 \|- I - 8I - 16I - 9I - 1) ---R + ---R +-----+ 2 +-------+ +-------+ 3 2 ---R \|I - 1 log((- 2I - 2I)\|- I - 1 \|- I + 1 - 2I - 2I + I + 1) ---R + ---R +-------+ +-----+ ---R +-------+ \|- I + 1 \|I - 1 ---R - 4\|- I - 1 log(- ------------------) ---R 2I - 2 ---R + ---R +---+ +-----+ ---R +-------+ \|- I \|I - 1 ---R 4\|- I - 1 atan(--------------) ---R I - 1 ---R + ---R +-------+ +-------+ +-------+ +---+ +-----+ ---R (- 8\|- I - 1 \|- I + 1 + 8\|- I - 1 \|- I )\|I - 1 ---R / ---R +-------+ +-----+ ---R 4\|- I - 1 \|I - 1 ---R , ---R + infinity, ---R ---R +-------+ +-----+ +-------+ +-----+ ---R +-----+ \|- I + 1 \|I - 1 +-----+ \|- I + 1 \|I + 1 ---R - \|I + 1 log(- ------------------) + \|I - 1 atan(------------------) ---R 2I - 2 I + 1 ---R + ---R +---+ +-----+ +---+ +-----+ ---R +-----+ \|- I \|I + 1 +-----+ \|- I \|I - 1 ---R - \|I - 1 atan(--------------) + \|I + 1 atan(--------------) ---R I + 1 I - 1 ---R + ---R +-------+ +---+ +-----+ +-----+ ---R (- 2\|- I + 1 + 2\|- I )\|I - 1 \|I + 1 ---R / ---R +-----+ +-----+ ---R \|I - 1 \|I + 1 ---R ] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 107 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 83 ---S 108 of 267 -in1721a:=integrate(-z^2/(z^2-1)/(1/(z-I))^(1/2), z= 0..1,"noPole") ---R ---R ---R (106) ---R [ + infinity, + infinity, ---R ---R +-------+ +-------+ +-------+ 2 ---R 3\|- I - 1 log(2I\|- I - 1 \|- I + 1 + 2I - 1) ---R + ---R +-------+ +-------+ +---+ 2 ---R - 3\|- I - 1 log((8I + 4)\|- I - 1 \|- I + 8I + 8I + 1) ---R + ---R +-------+ +---+ ---R +-----+ \|- I + 1 +-----+ \|- I ---R 12\|I - 1 log(- ----------) - 12\|I - 1 atan(--------) ---R +-----+ +-----+ ---R 2\|I - 1 \|I - 1 ---R + ---R +-------+ +---+ ---R (8I - 8)\|- I + 1 - 8I\|- I ---R / ---R 12 ---R , ---R ---R +-------+ +---+ ---R +-----+ \|- I + 1 +-----+ \|- I ---R 3\|I - 1 log(- ----------) - 3\|I - 1 atan(--------) ---R +-----+ +-----+ ---R 2\|I - 1 \|I - 1 ---R + ---R +-------+ +---+ ---R +-----+ \|- I + 1 +-----+ \|- I ---R - 3\|I + 1 atan(----------) + 3\|I + 1 atan(--------) ---R +-----+ +-----+ ---R \|I + 1 \|I + 1 ---R + ---R +-------+ +---+ ---R (2I - 2)\|- I + 1 - 2I\|- I ---R / ---R 3 ---R ] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 108 +--S 84 of 224 +in1720a:=integrate(-z^2/(z^2-1)*(1/(z-%i))^(1/2), z= 0..1,"noPole") +--R +--R +--R (84) +--R +------+ +------+ +--R | 1 | 1 +------+ +--R - %i |------ log((2 - 2%i) |------ \|1 - %i - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | %i | %i +------+ +--R |------ log((2 - 2%i) |------ \|1 - %i + 2 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | 1 +----+ | 1 +--R %i |------ log((2 - 2%i)\|- %i |------ - 1 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | %i | %i +----+ +--R - |------ log((2 - 2%i) |------ \|- %i + 1 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | %i | %i +----+ +--R |------ log((- 2 + 2%i) |------ \|- %i + 1 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | 1 +----+ | 1 +--R - %i |------ log((- 2 + 2%i)\|- %i |------ - 1 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | %i | %i +------+ +--R - |------ log((- 2 + 2%i) |------ \|1 - %i + 2 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | 1 | 1 +------+ +------+ +----+ +--R %i |------ log((- 2 + 2%i) |------ \|1 - %i - 2%i) - 8\|1 - %i + 8\|- %i +--R \|1 + %i \|1 + %i +--R / +--R 4 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 84 ---S 109 of 267 -in1723a:=integrate(-z^2/(z^2-1)*(1+I/z)^(1/2), z= 0..1,"noPole") +--S 85 of 224 +in1721a:=integrate(-z^2/(z^2-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole") --R --R ---R (107) ---R [ + infinity, + infinity, ---R ---R +-----+ ---R +-----+ +-+ +-------+ \|I + 1 ---R - 2I log(\|I + 1 + 1) + 2I log(\|I ) + 4\|- I - 1 log(- -----------) ---R +-------+ ---R 2\|- I - 1 ---R + ---R +-----+ ---R I log(- 2\|I + 1 + I + 2) ---R + ---R +-------+ +-------+ +-----+ 2 +-----+ ---R \|- I + 1 log(- 2\|- I + 1 \|I + 1 - I + 2) - 4\|I + 1 ---R + ---R 2 +-------+ +-------+ ---R - log(I )\|- I + 1 - 2%pi\|- I - 1 - I log(I) ---R / ---R 4 ---R , ---R ---R +-----+ ---R +-----+ +-+ +-------+ \|I + 1 ---R - 2I log(\|I + 1 + 1) + 2I log(\|I ) + 4\|- I - 1 log(- -----------) ---R +-------+ ---R 2\|- I - 1 ---R + ---R +-----+ ---R +-----+ +-----+ \|I - 1 +-----+ ---R I log(- 2\|I + 1 + I + 2) + 4\|I - 1 atan(--------) - 4\|I + 1 ---R +-----+ ---R \|I + 1 ---R + ---R +-------+ ---R - 2%pi\|- I - 1 - I log(I) ---R / ---R 4 ---R ] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 109 +--R (85) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 85 ---S 110 of 267 -in1724a:=integrate(-z^2/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z= 0..1,"noPole") +--S 86 of 224 +in1723a:=integrate(-z^2/(z^2-1)*(1+%i/z)^(1/2), z= 0..1,"noPole") --R --R ---R +----------+ ---R +-+ | +-+ ---R (4\|I - 12I + 8)\|- \|I + 1 - 8 ---R (108) ---------------------------------- ---R 15I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 110 +--R (86) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 86 ---S 111 of 267 +--S 87 of 224 in1731:=integrate(-log(1-z^2)*atanh(z), z= 0..1) --R --R ---R 2 ---R - log(4) + 4log(4) ---R (109) ------------------- ---R 4 +--R 2 +--R - log(4) + 4log(4) +--R (87) ------------------- +--R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 111 +--E 87 ---S 112 of 267 +--S 88 of 224 in1793a:=integrate((1-z^(1/2))^(1/2)*acoth(z^(1/2)), z= 0..1,"noPole") --R --R ---R +-+ +-+ ---R - 2\|2 log(12\|2 + 17) + 16 ---R (110) ---------------------------- ---R 15 +--R +-+ +-+ +--R - 2\|2 log(12\|2 + 17) + 16 +--R (88) ---------------------------- +--R 15 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 112 +--E 88 ---S 113 of 267 +--S 89 of 224 in1794a:=integrate((1-z^(1/2))^(1/2)*acoth(1-z^(1/2)), z= 0..1,"noPole") --R --R ---R - 4log(2) - 8%pi + 32 ---R (111) --------------------- ---R 15 +--R - 4log(2) - 8%pi + 32 +--R (89) --------------------- +--R 15 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 113 +--E 89 ---S 114 of 267 +--S 90 of 224 in1796a:=integrate((1+(1-z)^(1/2))^(1/2), z= 0..1,"noPole") --R --R ---R +-+ ---R 8\|2 + 8 ---R (112) --------- ---R 15 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 114 - ---S 115 of 267 -in183:=integrate(1/z, z= I..2*I) ---R ---R ---R 2 2 ---R log(4I ) - log(I ) ---R (113) ------------------ ---R 2 +--R +-+ +--R 8\|2 + 8 +--R (90) --------- +--R 15 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 115 +--E 90 ---S 116 of 267 -in184:=integrate(exp(I*z), z= I..2*I) +--S 91 of 224 +in184:=integrate(exp(%i*z), z= %i..2*%i) --R --R ---R 2 2 ---R 2I I ---R %e - %e ---R (114) ------------ ---R I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 116 +--R 2 +--R %i %e - %i %e +--R (91) -------------- +--R 2 +--R %e %e +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 91 ---S 117 of 267 +--S 92 of 224 in184a:=integrate(exp(%i*z), z= %i..2*%i) --R --R ---R 2 ---R %i %e - %i %e ---R (115) -------------- ---R 2 ---R %e %e +--R 2 +--R %i %e - %i %e +--R (92) -------------- +--R 2 +--R %e %e --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 117 +--E 92 ---S 118 of 267 -in187a:=integrate(2^log(z), z= -I..I,"noPole") +--S 93 of 224 +in187a:=integrate(2^log(z), z= -%i..%i,"noPole") --R --R ---R log(2)log(I) log(2)log(- I) ---R I %e + I %e ---R (116) ------------------------------------- ---R log(2) + 1 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 118 +--R log(%i)log(2) log(- %i)log(2) +--R %i %e + %i %e +--R (93) ----------------------------------------- +--R log(2) + 1 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 93 ---S 119 of 267 +--S 94 of 224 in187a:=integrate(2^log(z), z= -%i..%i,"noPole") --R --R ---R log(%i)log(2) log(- %i)log(2) ---R %i %e + %i %e ---R (117) ----------------------------------------- ---R log(2) + 1 +--R log(%i)log(2) log(- %i)log(2) +--R %i %e + %i %e +--R (94) ----------------------------------------- +--R log(2) + 1 --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 119 +--E 94 ---S 120 of 267 +--S 95 of 224 in194a:=integrate(sqrt(z^2), z= 1..2,"noPole") --R --R ---R 3 ---R (118) - ---R 2 +--R 3 +--R (95) - +--R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 120 +--E 95 ---S 121 of 267 -in1854a:=integrate(1/(z-1)/(1/(z-I))^(1/2), z= 0..1,"noPole") +--S 96 of 224 +in1854a:=integrate(1/(z-1)/(1/(z-%i))^(1/2), z= 0..1,"noPole") --R --R ---R (119) ---R [- infinity, +--R (96) +--R [ + infinity, --R ---R +-------+ +---+ ---R +-----+ \|- I + 1 +-----+ \|- I +-------+ ---R - 2\|I - 1 log(- ----------) + 2\|I - 1 atan(--------) + 2\|- I + 1 ---R +-----+ +-----+ ---R 2\|I - 1 \|I - 1 +--R +------+ +----+ +--R +---------+ \|1 - %i +---------+ 2\|- %i +--R - \|- 4 + 4%i log(- ------------) + \|- 4 + 4%i atan(------------) +--R +---------+ +---------+ +--R \|- 4 + 4%i \|- 4 + 4%i --R + ---R +---+ ---R - 2\|- I +--R +------+ +----+ +--R 2\|1 - %i - 2\|- %i --R ] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 121 +--R Type: Union(f2: List OrderedCompletion Expression Complex Integer,...) +--E 96 ---S 122 of 267 -in1856a:=integrate(1/(z-1)/(1-I*z)^(1/2), z= 0..1,"noPole") +--S 97 of 224 +in1856a:=integrate(1/(z-1)/(1-%i*z)^(1/2), z= 0..1,"noPole") --R --R ---R +-------+ +-----+ +-----+ ---R \|- I + 1 \|I - 1 \|I - 1 ---R 2log(- ------------------) - 2atan(--------) ---R 2I - 2 I - 1 ---R (120) [- infinity,--------------------------------------------] ---R +-----+ ---R \|I - 1 ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 122 +--R (97) +--R [ + infinity, +--R +------+ +--R +---------+ %i\|1 - %i +---------+ 1 + %i +--R - \|- 2 - 2%i log(- --------------------) + \|- 2 - 2%i atan(------------)] +--R +---------+ +---------+ +--R (1 + %i)\|- 2 - 2%i \|- 2 - 2%i +--R Type: Union(f2: List OrderedCompletion Expression Complex Integer,...) +--E 97 ---S 123 of 267 used to work -in1859a:=integrate(1/(z^2-1)*(1+1/z^3)^(1/2), z= 0..1,"noPole") ---R ---R ---R (121) "failed" ---R Type: Union(fail: failed,...) ---E 123 --- --- +-------------------+ --- | 2 --- (- \|- 3%%EM0 - 2 + 6%i - %%EM0) --- * --- log --- +--+ +--+ --- ((8 + 72%i)\|%i + 10 + 8%i)%%EM0 + (- 2 - 18%i)\|%i + 2 --- + --- 18%i --- * --- +-------------------+ --- | 2 --- \|- 3%%EM0 - 2 + 6%i --- + --- +--+ 2 --- ((- 8 - 72%i)\|%i - 10 - 8%i)%%EM0 --- + --- +--+ +--+ --- ((- 2 - 18%i)\|%i + 2 + 18%i)%%EM0 + (- 128 - 4%i)\|%i - 68 --- + --- - 120%i --- + --- +-------------------+ --- | 2 --- (\|- 3%%EM0 - 2 + 6%i + %%EM0) --- * --- log --- +-------------------+ --- | 2 --- ((10 + 8%i)%%EM0 + 2 + 18%i)\|- 3%%EM0 - 2 + 6%i --- + --- 2 --- (- 10 - 8%i)%%EM0 + (2 + 18%i)%%EM0 - 50 - 40%i --- + --- +-------------------+ --- | 2 --- (- \|- 3%%EM0 - 2 + 6%i + %%EM0) --- * --- log --- +-------------------+ --- | 2 --- ((- 10 - 8%i)%%EM0 - 2 - 18%i)\|- 3%%EM0 - 2 + 6%i --- + --- 2 --- (- 10 - 8%i)%%EM0 + (2 + 18%i)%%EM0 - 50 - 40%i --- + --- +-------------------+ --- | 2 --- (\|- 3%%EM0 - 2 + 6%i - %%EM0) --- * --- log --- +--+ +--+ --- ((- 8 - 72%i)\|%i - 10 - 8%i)%%EM0 + (2 + 18%i)\|%i - 2 --- + --- - 18%i --- * --- +-------------------+ --- | 2 --- \|- 3%%EM0 - 2 + 6%i --- + --- +--+ 2 --- ((- 8 - 72%i)\|%i - 10 - 8%i)%%EM0 --- + --- +--+ +--+ --- ((- 2 - 18%i)\|%i + 2 + 18%i)%%EM0 + (- 128 - 4%i)\|%i - 68 --- + --- - 120%i --- + --- 2%%EM0 --- * --- log --- +--+ 2 --- ((72 - 8%i)\|%i + 8 - 10%i)%%EM0 --- + --- +--+ +--+ --- ((18 - 2%i)\|%i - 18 + 2%i)%%EM0 + (22 - 48%i)\|%i - 71 + 17%i --- + --- 2 --- - 2%%EM0 log((8 - 10%i)%%EM0 + (- 18 + 2%i)%%EM0 - 31 + 8%i) --- / --- 4 --- Type: Union(f1: OrderedCompletion Expression Complex Integer,...) - ---S 124 of 267 -in1863a:=integrate(1/(z^2-1)*(1/(z-I))^(1/2), z= 0..1,"noPole") ---R ---R ---R (122) ---R [- infinity, ---R ---R +-----+ 2 +-------+ +-------+ 3 2 ---R \|I - 1 log((2I + 2I)\|- I - 1 \|- I + 1 - 2I - 2I + I + 1) ---R + ---R +-----+ 2 +-------+ +---+ 3 2 ---R - \|I - 1 log((8I + 12I + 4)\|- I - 1 \|- I - 8I - 16I - 9I - 1) ---R + ---R +-------+ +-----+ +---+ +-----+ ---R +-------+ \|- I + 1 \|I - 1 +-------+ \|- I \|I - 1 ---R 4\|- I - 1 log(- ------------------) - 4\|- I - 1 atan(--------------) ---R 2I - 2 I - 1 ---R / ---R +-------+ +-----+ ---R 4\|- I - 1 \|I - 1 ---R , ---R - infinity, ---R ---R +-------+ +-----+ +-------+ +-----+ ---R +-----+ \|- I + 1 \|I - 1 +-----+ \|- I + 1 \|I + 1 ---R \|I + 1 log(- ------------------) - \|I - 1 atan(------------------) ---R 2I - 2 I + 1 ---R + ---R +---+ +-----+ +---+ +-----+ ---R +-----+ \|- I \|I + 1 +-----+ \|- I \|I - 1 ---R \|I - 1 atan(--------------) - \|I + 1 atan(--------------) ---R I + 1 I - 1 ---R / ---R +-----+ +-----+ ---R \|I - 1 \|I + 1 ---R ] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 124 +--S 98 of 224 +in1863a:=integrate(1/(z^2-1)*(1/(z-%i))^(1/2), z= 0..1,"noPole") +--R +--R +--R (98) +--R +------+ +------+ +--R | 1 | 1 +------+ +--R %i |------ log((2 - 2%i) |------ \|1 - %i - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | %i | %i +------+ +--R - |------ log((2 - 2%i) |------ \|1 - %i + 2 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | 1 +----+ | 1 +--R - %i |------ log((2 - 2%i)\|- %i |------ - 1 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | %i | %i +----+ +--R |------ log((2 - 2%i) |------ \|- %i + 1 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | %i | %i +----+ +--R - |------ log((- 2 + 2%i) |------ \|- %i + 1 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | 1 +----+ | 1 +--R %i |------ log((- 2 + 2%i)\|- %i |------ - 1 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | %i | %i +------+ +--R |------ log((- 2 + 2%i) |------ \|1 - %i + 2 - 2%i) +--R \|1 + %i \|1 + %i +--R + +--R +------+ +------+ +--R | 1 | 1 +------+ +--R - %i |------ log((- 2 + 2%i) |------ \|1 - %i - 2%i) +--R \|1 + %i \|1 + %i +--R / +--R 4 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 98 ---S 125 of 267 +--S 99 of 224 in1864a:=integrate(1/(z^2-1)*((1+z)/(z-1))^(1/3), z= 0..1,"noPole") --R --R ---R (123) + infinity +--R (99) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 125 - ---S 126 of 267 -in1866a:=integrate(1/(z^2-1)*(1-I/z)^(1/2), z= 0..1,"noPole") ---R ---R ---R (124) ---R [- infinity, ---R ---R +-----+ ---R +-----+ +-------+ +-----+ 2 +-----+ \|I - 1 ---R \|I + 1 log(2\|- I + 1 \|I + 1 - I + 2) + 4\|I - 1 log(- -----------) ---R +-------+ ---R 2\|- I + 1 ---R + ---R 2 +-----+ ---R - log(I )\|I + 1 ---R / ---R 4 ---R , ---R - infinity, ---R +-----+ +-------+ ---R +-----+ \|I - 1 +-------+ \|- I + 1 +-------+ ---R 2\|I - 1 log(- -----------) + 2\|- I - 1 atan(----------) - %pi\|- I - 1 ---R +-------+ +-------+ ---R 2\|- I + 1 \|- I - 1 ---R -------------------------------------------------------------------------] ---R 2 ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 126 - ---S 127 of 267 -in1867a:=integrate(1/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z= 0..1,"noPole") ---R ---R ---R (125) 0 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 127 +--E 99 ---S 128 of 267 -in1869a:=integrate(1/(z^2-1)*(1-1/(I*z)^(1/2))^(1/2), z= 0..1,"noPole") +--S 100 of 224 +in1866a:=integrate(1/(z^2-1)*(1-%i/z)^(1/2), z= 0..1,"noPole") --R --R ---R (126) 0 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 128 +--R (100) - infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 100 ---S 129 of 267 -in1870a:=integrate(1/(z^2-1)/(1+(I*z)^(1/2))^(1/2), z= 0..1,"noPole") +--S 101 of 224 +in1870a:=integrate(1/(z^2-1)/(1+(%i*z)^(1/2))^(1/2), z= 0..1,"noPole") --R --R ---R (127) 0 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 129 +--R (101) +--R - +--R +-------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +---------+ +--R | +-+ +---------+ +--R +-+ |3\|2 + 4 +-+ | +--+ +--R ((48\|2 - 64) |--------- - 4%i\|2 )\|\|%i + 1 +--R | +-+ +--R \| 16\|2 +--R * +--R +-------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--+ +-+ +--R (- 16%i\|2 + 16%i) |--------- + (4\|%i + 8)\|2 - 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R +-------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +-------------------+ +--R +---------+ | +---------+ +--R | +-+ | | +-+ +--R +-+ |3\|2 + 4 +-+ | |3\|2 + 4 +--R ((48\|2 - 64) |--------- - 4%i\|2 ) |4%i |--------- + 1 +--R | +-+ | | +-+ +--R \| 16\|2 \| \| 16\|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +-+ +--R (- 16%i\|2 + 16%i) |--------- + 8\|2 - 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +-------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +-----------+ +--R | +-+ +---------+ +--R +-+ |- 3\|2 + 4 +-+ | +--+ +--R ((48%i\|2 + 64%i) |----------- + 4%i\|2 )\|\|%i + 1 +--R | +-+ +--R \| 16\|2 +--R * +--R +-------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +--+ +-+ +--R (- 16\|2 - 16) |----------- + (4\|%i + 8)\|2 + 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R +-------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +-+ +--R ((48%i\|2 + 64%i) |----------- + 4%i\|2 ) +--R | +-+ +--R \| 16\|2 +--R * +--R +-------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +-+ +--R (- 16\|2 - 16) |----------- + 8\|2 + 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R +---------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |- 4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +-----------+ +--R | +-+ +---------+ +--R +-+ |- 3\|2 + 4 +-+ | +--+ +--R ((48%i\|2 + 64%i) |----------- - 4%i\|2 )\|\|%i + 1 +--R | +-+ +--R \| 16\|2 +--R * +--R +---------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |- 4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +--+ +-+ +--R (16\|2 + 16) |----------- + (4\|%i + 8)\|2 + 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +---------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |- 4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +-+ +--R ((48%i\|2 + 64%i) |----------- - 4%i\|2 ) +--R | +-+ +--R \| 16\|2 +--R * +--R +---------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |- 4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +-+ +--R (16\|2 + 16) |----------- + 8\|2 + 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R +---------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |- 4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +---------+ +--R | +-+ +---------+ +--R +-+ |3\|2 + 4 +-+ | +--+ +--R ((48\|2 - 64) |--------- + 4%i\|2 )\|\|%i + 1 +--R | +-+ +--R \| 16\|2 +--R * +--R +---------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |- 4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--+ +-+ +--R (16%i\|2 - 16%i) |--------- + (4\|%i + 8)\|2 - 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +---------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |- 4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +---------------------+ +--R +---------+ | +---------+ +--R | +-+ | | +-+ +--R +-+ |3\|2 + 4 +-+ | |3\|2 + 4 +--R ((48\|2 - 64) |--------- + 4%i\|2 ) |- 4%i |--------- + 1 +--R | +-+ | | +-+ +--R \| 16\|2 \| \| 16\|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +-+ +--R (16%i\|2 - 16%i) |--------- + 8\|2 - 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R +---------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |- 4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +---------------------+ +--R +---------+ | +---------+ +--R | +-+ | | +-+ +--R +-+ |3\|2 + 4 +-+ | |3\|2 + 4 +--R ((- 48\|2 + 64) |--------- - 4%i\|2 ) |- 4%i |--------- + 1 +--R | +-+ | | +-+ +--R \| 16\|2 \| \| 16\|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +-+ +--R (16%i\|2 - 16%i) |--------- + 8\|2 - 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +---------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |- 4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +---------+ +--R | +-+ +---------+ +--R +-+ |3\|2 + 4 +-+ | +--+ +--R ((- 48\|2 + 64) |--------- - 4%i\|2 )\|\|%i + 1 +--R | +-+ +--R \| 16\|2 +--R * +--R +---------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |- 4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--+ +-+ +--R (16%i\|2 - 16%i) |--------- + (4\|%i + 8)\|2 - 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R +---------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |- 4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +-+ +--R ((- 48%i\|2 - 64%i) |----------- + 4%i\|2 ) +--R | +-+ +--R \| 16\|2 +--R * +--R +---------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |- 4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +-+ +--R (16\|2 + 16) |----------- + 8\|2 + 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +---------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |- 4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +-----------+ +--R | +-+ +---------+ +--R +-+ |- 3\|2 + 4 +-+ | +--+ +--R ((- 48%i\|2 - 64%i) |----------- + 4%i\|2 )\|\|%i + 1 +--R | +-+ +--R \| 16\|2 +--R * +--R +---------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |- 4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +--+ +-+ +--R (16\|2 + 16) |----------- + (4\|%i + 8)\|2 + 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +-------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +-+ +--R ((- 48%i\|2 - 64%i) |----------- - 4%i\|2 ) +--R | +-+ +--R \| 16\|2 +--R * +--R +-------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +-+ +--R (- 16\|2 - 16) |----------- + 8\|2 + 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R +-------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +-----------+ +--R | +-+ +---------+ +--R +-+ |- 3\|2 + 4 +-+ | +--+ +--R ((- 48%i\|2 - 64%i) |----------- - 4%i\|2 )\|\|%i + 1 +--R | +-+ +--R \| 16\|2 +--R * +--R +-------------------+ +--R | +-----------+ +--R | | +-+ +--R | |- 3\|2 + 4 +--R |4 |----------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +-----------+ +--R | +-+ +--R +-+ |- 3\|2 + 4 +--+ +-+ +--R (- 16\|2 - 16) |----------- + (4\|%i + 8)\|2 + 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R - +--R +-------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +-------------------+ +--R +---------+ | +---------+ +--R | +-+ | | +-+ +--R +-+ |3\|2 + 4 +-+ | |3\|2 + 4 +--R ((- 48\|2 + 64) |--------- + 4%i\|2 ) |4%i |--------- + 1 +--R | +-+ | | +-+ +--R \| 16\|2 \| \| 16\|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +-+ +--R (- 16%i\|2 + 16%i) |--------- + 8\|2 - 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R + +--R +-------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R * +--R log +--R +---------+ +--R | +-+ +---------+ +--R +-+ |3\|2 + 4 +-+ | +--+ +--R ((- 48\|2 + 64) |--------- + 4%i\|2 )\|\|%i + 1 +--R | +-+ +--R \| 16\|2 +--R * +--R +-------------------+ +--R | +---------+ +--R | | +-+ +--R | |3\|2 + 4 +--R |4%i |--------- + 1 +--R | | +-+ +--R \| \| 16\|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--+ +-+ +--R (- 16%i\|2 + 16%i) |--------- + (4\|%i + 8)\|2 - 4 +--R | +-+ +--R \| 16\|2 +--R / +--R +-+ +--R \|2 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 101 --S 130 -in1872a:=integrate(1/(z^2-1)/(I/(z+I))^(1/2), z= 0..1,"noPole") +--S 102 of 224 +in1872a:=integrate(1/(z^2-1)/(%i/(z+%i))^(1/2), z= 0..1,"noPole") --R --R ---R (128) ---R [ + infinity, + infinity, ---R ---R +-----+ +-----+ +-----+ ---R |I - 1 2 |I - 1 | I 2 ---R |----- log((2I + 2I) |----- |----- + 2I - 1) ---R \| I \| I \|I + 1 ---R + ---R +-----+ +-----+ ---R |I - 1 2 |I - 1 2 ---R - |----- log((8I - 4I) |----- + 8I - 8I + 1) ---R \| I \| I ---R + ---R +-----+ ---R | I ---R +-------+ (- I - 1) |----- +-------+ ---R |- I - 1 \|I + 1 |- I - 1 I + 1 ---R - 4 |------- log(----------------- + 4 |------- atan(-----------) ---R \| I +-------+ \| I +-------+ ---R |- I - 1 |- I - 1 ---R 2I |------- I |------- ---R \| I \| I ---R / ---R 4 ---R , ---R ---R +-----+ +-----+ ---R | I | I ---R +-------+ (- I - 1) |----- +-------+ (I - 1) |----- ---R |- I - 1 \|I + 1 |- I + 1 \|I + 1 ---R - |------- log(-----------------) + |------- atan(---------------) ---R \| I +-------+ \| I +-------+ ---R |- I - 1 |- I + 1 ---R 2I |------- I |------- ---R \| I \| I ---R + ---R +-------+ +-------+ ---R |- I - 1 I + 1 |- I + 1 I - 1 ---R |------- atan(-----------) - |------- atan(-----------) ---R \| I +-------+ \| I +-------+ ---R |- I - 1 |- I + 1 ---R I |------- I |------- ---R \| I \| I ---R ] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 130 +--R (102) +--R +------+ +--R +------+ | %i +------+ +--R \|1 + %i log((2 + 2%i) |------ \|1 + %i + 2%i) +--R \|1 + %i +--R + +--R +------+ +------+ +--R - \|1 + %i log((2 + 2%i)\|1 + %i + 1 + 3%i) +--R + +--R +------+ +--R +------+ | %i +------+ +--R \|1 - %i log((2 - 2%i) |------ \|1 - %i - 2 + 2%i) +--R \|1 + %i +--R + +--R +------+ +------+ +--R - \|1 - %i log((2 - 2%i)\|1 - %i - 1 + 3%i) +--R + +--R +------+ +------+ +--R \|1 - %i log((- 2 + 2%i)\|1 - %i - 1 + 3%i) +--R + +--R +------+ +--R +------+ | %i +------+ +--R - \|1 - %i log((- 2 + 2%i) |------ \|1 - %i - 2 + 2%i) +--R \|1 + %i +--R + +--R +------+ +------+ +--R \|1 + %i log((- 2 - 2%i)\|1 + %i + 1 + 3%i) +--R + +--R +------+ +--R +------+ | %i +------+ +--R - \|1 + %i log((- 2 - 2%i) |------ \|1 + %i + 2%i) +--R \|1 + %i +--R / +--R 4 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 102 ---S 131 of 267 +--S 103 of 224 in1933a:=integrate(atan(z)/z/(z*(1+z))^(1/2), z= 0..1,"noPole") --R --R ---R (129) +--R (103) --R +-+ 4+-+ %pi --R (\|2 - 1)\|2 cos(---) --R 8 @@ -3779,71 +3934,69 @@ in1933a:=integrate(atan(z)/z/(z*(1+z))^(1/2), z= 0..1,"noPole") --R +-+ --R 2\|2 - 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 131 +--E 103 ---S 132 of 267 +--S 104 of 224 in1945a:=integrate(acoth((1-z)/(1+z)), z= 0..1,"noPole") --R --R --R 1 ---R (130) - +--R (104) - --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 132 +--E 104 ---S 133 of 267 +--S 105 of 224 in1946a:=integrate(acoth((1-z)/(1+z))*z, z= 0..1,"noPole") --R --R --R 1 ---R (131) - +--R (105) - --R 8 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 133 +--E 105 ---S 134 of 267 +--S 106 of 224 in1947a:=integrate(acoth((1-z)/(1+z))*z^(1/2), z= 0..1,"noPole") --R --R --R 2 ---R (132) - +--R (106) - --R 9 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 134 +--E 106 ---S 135 of 267 +--S 107 of 224 in1950a:=integrate(acoth((1-z)/(1+z))/(1-z)^(1/2), z= 0..1,"noPole") --R --R --R - log(4) - 2log(2) + 4 ---R (133) ---------------------- +--R (107) ---------------------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 135 +--E 107 ---S 136 of 267 -in1952a:=integrate(acoth((1-z)/(1+z))*(I*z)^(1/2), z= 0..1,"noPole") +--S 108 of 224 +in1952a:=integrate(acoth((1-z)/(1+z))*(%i*z)^(1/2), z= 0..1,"noPole") --R --R ---R +-+ ---R 2\|I ---R (134) ----- ---R 9 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 136 +--R +--+ +--R 2\|%i +--R (108) ------ +--R 9 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 108 ---S 137 of 267 -in1954a:=integrate(acoth((1-z)/(1+z))/(I*z)^(1/2), z= 0..1,"noPole") +--S 109 of 224 +in1954a:=integrate(acoth((1-z)/(1+z))/(%i*z)^(1/2), z= 0..1,"noPole") --R --R ---R +-+ ---R 2\|I ---R (135) ----- ---R I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 137 +--R +--+ +--R (109) - 2%i\|%i +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 109 ---S 138 of 267 +--S 110 of 224 in202a:=integrate(acsc(z), z= 0..1/2,"noPole") --R --R @@ -3851,16 +4004,16 @@ in202a:=integrate(acsc(z), z= 0..1/2,"noPole") --R +-+ 2\|2 \|3 +-+ --R - 6\|2 atan(---------) - 3atan(4\|3 ) + 2%pi --R 5 ---R (136) -------------------------------------------- +--R (110) -------------------------------------------- --R 12 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 138 +--E 110 ---S 139 of 267 +--S 111 of 224 in206a:=integrate(sqrt(1-1/z), z= %pi..2*%pi,"noPole") --R --R ---R (137) +--R (111) --R +--------+ +-------+ --R |2%pi - 1 |%pi - 1 --R - 2log( |-------- + 1) + 2log( |------- + 1) @@ -3880,24 +4033,24 @@ in206a:=integrate(sqrt(1-1/z), z= %pi..2*%pi,"noPole") --R / --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 139 +--E 111 ---S 140 of 267 +--S 112 of 224 in211:=integrate(acos(sin(2*z))*cos(z), z= 0..4*%pi/3) --R --R --R +-+ --R 13%pi\|3 + 36 ---R (138) -------------- +--R (112) -------------- --R 12 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 140 +--E 112 ---S 141 of 267 +--S 113 of 224 in213a:=integrate(log(abs(1+1/(-z)^(1/3))), z= 0..1,"noPole") --R --R ---R (139) +--R (113) --R 3+---+2 3+---+ --R 3+---+2 3+---+ \|- 1 + 2\|- 1 + 1 3+---+2 3+---+ --R - log(\|- 1 + 2\|- 1 + 1) + log(---------------------) - \|- 1 + 2\|- 1 @@ -3906,149 +4059,100 @@ in213a:=integrate(log(abs(1+1/(-z)^(1/3))), z= 0..1,"noPole") --R ----------------------------------------------------------------------------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 141 +--E 113 ---S 142 of 267 +--S 114 of 224 in216a:=integrate(1/(1/z-1)^(1/3), z= 0..1,"noPole") --R --R --R 2%pi ---R (140) ----- +--R (114) ----- --R +-+ --R 3\|3 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 142 +--E 114 ---S 143 of 267 +--S 115 of 224 in2023a:=integrate((1-z)/(-1+z^(1/2)), z= 1..2,"noPole") --R --R --R +-+ --R - 4\|2 - 1 ---R (141) ----------- +--R (115) ----------- --R 3 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 143 +--E 115 ---S 144 of 267 +--S 116 of 224 in2024a:=integrate(log(1-1/z)+csc(z-1), z= 0..1,"noPole") --R --R ---R (142) - infinity +--R (116) - infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 144 +--E 116 ---S 145 of 267 +--S 117 of 224 in2032a:=integrate(acoth(z)/z^(1/2), z= 0..1,"noPole") --R --R --R - 2log(2) + %pi ---R (143) --------------- +--R (117) --------------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 145 +--E 117 ---S 146 of 267 +--S 118 of 224 in2040a:=integrate(log(1-1/z^4)+cot(z), z= -1..1,"noPole") --R --R ---R (144) log(16) + log(4) + %pi +--R (118) log(16) + log(4) + %pi --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 146 +--E 118 ---S 147 of 267 +--S 119 of 224 in2050a:=integrate(-csc(z-1)-1/z^(1/3), z= -1..1,"noPole") --R --R ---R (145) + infinity +--R (119) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 147 +--E 119 ---S 148 of 267 -in2051a:=integrate((z^2+I*z-1)^(1/2)*z, z= -1..1,"noPole") +--S 120 of 224 +in2051a:=integrate((z^2+%i*z-1)^(1/2)*z, z= -1..1,"noPole") --R --R ---R (146) ---R 7 5 3 +---+ 8 7 6 ---R (108I - 1776I - 7104I + 6912I)\|- I - 18I + 228I + 936I ---R + ---R 5 4 3 2 ---R - 1104I + 2208I - 7488I - 7296I + 2304I ---R * ---R +-+ ---R \|I ---R + ---R 8 7 6 5 4 3 2 ---R - 18I - 228I + 936I + 1104I + 2208I + 7488I - 7296I ---R + ---R - 2304I ---R * ---R +---+ ---R \|- I +--R (120) +--R +----+ +--+ +----+ +--R (12132%i\|- %i + 8550 + 8460%i)\|%i + (8550 - 8460%i)\|- %i --R + ---R 9 7 3 ---R 3I - 744I + 11904I - 768I +--R - 11925%i --R * ---R +---+ 2 ---R log((- 4I + 8)\|- I + I - 8I + 4) +--R +----+ +--R log((8 - 4%i)\|- %i + 3 - 8%i) --R + ---R 7 5 3 +---+ 8 7 6 ---R (- 108I + 1776I + 7104I - 6912I)\|- I + 18I - 228I - 936I ---R + ---R 5 4 3 2 ---R 1104I - 2208I + 7488I + 7296I - 2304I ---R * ---R +-+ ---R \|I +--R +----+ +--+ +----+ +--R (- 12132%i\|- %i - 8550 - 8460%i)\|%i + (- 8550 + 8460%i)\|- %i --R + ---R 8 7 6 5 4 3 2 ---R (18I + 228I - 936I - 1104I - 2208I - 7488I + 7296I + 2304I) ---R * ---R +---+ ---R \|- I ---R + ---R 9 7 3 ---R - 3I + 744I - 11904I + 768I +--R 11925%i --R * ---R +-+ 2 ---R log((- 4I - 8)\|I + I + 8I + 4) +--R +--+ +--R log((- 8 - 4%i)\|%i + 3 + 8%i) --R + ---R 6 4 2 +---+ 8 7 6 5 ---R (1728I - 10752I - 5120I )\|- I - 12I - 424I + 2736I + 6816I ---R + ---R 4 3 2 ---R - 6208I + 1152I - 3840I - 512I ---R * ---R +-+ ---R \|I ---R + ---R 8 7 6 5 4 3 2 +---+ ---R (12I - 424I - 2736I + 6816I + 6208I + 1152I + 3840I - 512I)\|- I ---R + ---R 8 6 4 2 ---R 144I - 6848I + 3840I + 3072I +--R +----+ +--+ +----+ +--R (- 7360\|- %i - 5116 + 5576%i)\|%i + (5116 + 5576%i)\|- %i + 7760 --R / ---R 4 2 +---+ 5 4 3 2 ---R (3456I - 70656I + 55296)\|- I - 576I + 7296I + 32256I - 64512I ---R + ---R - 58368I + 18432 ---R * ---R +-+ ---R \|I ---R + ---R 5 4 3 2 +---+ 6 ---R (- 576I - 7296I + 32256I + 64512I - 58368I - 18432)\|- I + 96I +--R +----+ +--+ +----+ +--R (129408\|- %i + 90240 - 91200%i)\|%i + (- 90240 - 91200%i)\|- %i --R + ---R 4 2 ---R - 24192I + 96768I - 6144 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 148 +--R - 127200 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 120 ---S 149 of 267 +--S 121 of 224 in2053a:=integrate(atan(2*z-1), z= 0..infinity,"noPole") --R --R ---R (147) +--R (121) --R 4 3 2 --R - log(4infinity - 8infinity + 8infinity - 4infinity + 1) --R + @@ -4059,117 +4163,84 @@ in2053a:=integrate(atan(2*z-1), z= 0..infinity,"noPole") --R / --R 8 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 149 +--E 121 ---S 150 of 267 +--S 122 of 224 in2054:=integrate(atan(1/z^(1/2))+1, z= -1..1) +--R --R ---R 4 3 2 ---R - log(4infinity - 8infinity + 8infinity - 4infinity + 1) ---R + ---R 2infinity - 1 ---R (- 4infinity + 2)atan(----------------------) - %pi ---R 2 ---R 2infinity - 2infinity ---R / ---R 8 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---R NOTE: 150 USED TO WORK ---E 150 +--R (122) potentialPole +--R Type: Union(pole: potentialPole,...) +--E 122 ---S 151 of 267 +--S 123 of 224 in2056a:=integrate(z^(1/2)-acoth(1-z), z= 0..1,"noPole") --R --R --R - 3log(4) + 4 ---R (149) ------------- +--R (123) ------------- --R 6 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 151 +--E 123 ---S 152 of 267 -in2058a:=integrate((z^2+I*z-3)^(1/2)+z, z= -1..1,"noPole") +--S 124 of 224 +in2058a:=integrate((z^2+%i*z-3)^(1/2)+z, z= -1..1,"noPole") --R --R ---R (150) ---R 4 2 +-------+ 5 4 3 2 ---R (- 16I - 128I + 768)\|- I - 2 + 4I - 24I - 32I - 320I ---R + ---R - 960I - 384 ---R * ---R +-----+ ---R \|I - 2 ---R + ---R 5 4 3 2 +-------+ 6 4 ---R (4I + 24I - 32I + 320I - 960I + 384)\|- I - 2 - I + 60I +--R (124) +--R +--------+ +--------+ +--R (- 880\|- 2 - %i + 88 + 924%i)\|- 2 + %i --R + ---R 2 ---R 848I - 192 +--R +--------+ +--R (- 88 + 924%i)\|- 2 - %i + 979 --R * ---R +-------+ 2 ---R log((- 4I + 8)\|- I - 2 + I - 8I - 4) +--R +--------+ +--R log((8 - 4%i)\|- 2 - %i - 5 - 8%i) --R + ---R 4 2 +-------+ 5 4 3 2 ---R (16I + 128I - 768)\|- I - 2 - 4I + 24I + 32I + 320I + 960I ---R + ---R 384 ---R * ---R +-----+ ---R \|I - 2 ---R + ---R 5 4 3 2 +-------+ 6 4 ---R (- 4I - 24I + 32I - 320I + 960I - 384)\|- I - 2 + I - 60I +--R +--------+ +--------+ +--------+ +--R (880\|- 2 - %i - 88 - 924%i)\|- 2 + %i + (88 - 924%i)\|- 2 - %i --R + ---R 2 ---R - 848I + 192 +--R - 979 --R * ---R +-----+ 2 ---R log((- 4I - 8)\|I - 2 + I + 8I - 4) +--R +--------+ +--R log((- 8 - 4%i)\|- 2 + %i - 5 + 8%i) --R + ---R 3 +-------+ 5 4 3 2 ---R (- 256I + 1024I)\|- I - 2 + 4I + 72I - 288I - 1088I + 64I ---R + ---R 1152 ---R * ---R +-----+ ---R \|I - 2 ---R + ---R 5 4 3 2 +-------+ 5 3 ---R (- 4I + 72I + 288I - 1088I - 64I + 1152)\|- I - 2 - 32I + 768I +--R +--------+ +--------+ +--R (- 1280%i\|- 2 - %i - 2312 - 356%i)\|- 2 + %i --R + ---R - 2560I +--R +--------+ +--R (- 2312 + 356%i)\|- 2 - %i + 3360%i --R / ---R 2 +-------+ 3 2 +-----+ ---R ((256I - 1024)\|- I - 2 - 64I + 384I + 1280I + 512)\|I - 2 +--R +--------+ +--------+ +--------+ +--R (1280\|- 2 - %i - 128 - 1344%i)\|- 2 + %i + (128 - 1344%i)\|- 2 - %i --R + ---R 3 2 +-------+ 4 2 ---R (- 64I - 384I + 1280I - 512)\|- I - 2 + 16I - 1152I + 256 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 152 +--R - 1424 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 124 ---S 153 of 267 -in2068a:=integrate(1/(I*z)^(1/2)-csch(z), z= 0..1,"noPole") +--S 125 of 224 +in2068a:=integrate(1/(%i*z)^(1/2)-csch(z), z= 0..1,"noPole") --R --R ---R (151) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 153 +--R (125) - infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 125 ---S 154 of 267 +--S 126 of 224 in2071a:=integrate(1/(3+z)^3*acoth(z), z= -1..1,"noPole") --R --R --R - 3log(16) + 3log(4) - 2 ---R (152) ------------------------ +--R (126) ------------------------ --R 128 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 154 +--E 126 ---S 155 of 267 +--S 127 of 224 in2090a:=integrate(exp(z^(1/3))*(3+z)^9, z= -1..1,"noPole") --R --R ---R (153) +--R (127) --R 3+---+2 --R 13467752003249079711273325865856\|- 1 --R + @@ -4184,577 +4255,153 @@ in2090a:=integrate(exp(z^(1/3))*(3+z)^9, z= -1..1,"noPole") --R + --R - 9746099248106233432776547720320%e --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 155 +--E 127 ---S 156 of 267 +--S 128 of 224 in2094a:=integrate(asinh(z)-acoth(z), z= -1..1,"noPole") --R --R --R +-+ +-+ --R log(2\|2 + 3) + log(- 2\|2 + 3) ---R (154) --------------------------------- +--R (128) --------------------------------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 156 +--E 128 ---S 157 of 267 +--S 129 of 224 in2096a:=integrate(log(z)^2, z= %minusInfinity..%plusInfinity,"noPole") --R --R ---R (155) + infinity +--R (129) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 157 +--E 129 ---S 158 of 267 +--S 130 of 224 in2098a:=integrate(1/z^(1/3)-z^2/(z-1)^2, z= -1..1,"noPole") --R --R ---R (156) - infinity +--R (130) - infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 158 +--E 130 ---S 159 of 267 -in2105a:=integrate(-1/(z^2-I*z+2)^(1/2)/z, z= 0..1,"noPole") +--S 131 of 224 +in2105a:=integrate(-1/(z^2-%i*z+2)^(1/2)/z, z= 0..1,"noPole") --R --R ---R (157) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 159 +--R (131) - infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 131 ---S 160 of 267 +--S 132 of 224 in2106a:=integrate(acos(z)+acoth(1-z), z= 0..1,"noPole") --R --R --R log(4) + 2 ---R (158) ---------- +--R (132) ---------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 160 - ---S 161 of 267 -in2108a:=integrate((1-I/(1+I/z)^2)^(1/2), z= -1..1,"noPole") ---R ---R ---R (159) ---R [ ---R +-----------+ +----------+ ---R 2 | 2 3 2 | 2 ---R (I \|I - 3I + 1 - I + I )\|I + I + 1 ---R + ---R +-----------+ ---R 3 2 | 2 4 2 ---R (- I - I )\|I - 3I + 1 + I - I ---R * ---R log ---R 3 2 +-------+ 4 3 2 ---R ((4I - 4I + 2I - 2)\|- I + 1 - 2I + 4I - 6I + 4I) ---R * ---R +----------+ ---R | 2 ---R \|I + I + 1 ---R + ---R 4 3 2 +-------+ 5 4 3 2 ---R (- 4I + 2I - 2I + 4I)\|- I + 1 + 2I - 3I + 5I - 4I ---R + ---R 2I - 2 ---R / ---R +----------+ ---R | 2 2 ---R (2I + 2)\|I + I + 1 - 2I - 3I - 2 ---R + ---R +-----------+ ---R +---+ +-------+ | 2 2 +---+ +-------+ ---R (- I\|- I \|- I + 1 \|I - 3I + 1 + (I - I)\|- I \|- I + 1 ) ---R * ---R +----------+ ---R | 2 ---R \|I + I + 1 ---R + ---R +-----------+ ---R 2 +---+ +-------+ | 2 3 +---+ +-------+ ---R (I + I)\|- I \|- I + 1 \|I - 3I + 1 + (- I + I)\|- I \|- I + 1 ---R * ---R log ---R +-----------+ ---R 2 +---+ 3 2 | 2 ---R ((4I - 10I + 4)\|- I + 2I - 10I + 10I - 2)\|I - 3I + 1 ---R + ---R 3 2 +---+ 4 3 2 ---R (- 4I + 16I - 16I + 4)\|- I - 2I + 13I - 24I + 13I - 2 ---R / ---R +-----------+ ---R 3 2 | 2 4 3 2 ---R (2I - 6I + 6I - 2)\|I - 3I + 1 - 2I + 9I - 14I + 9I - 2 ---R + ---R +-----------+ ---R +---+ +-------+ | 2 2 +---+ +-------+ ---R (I\|- I \|- I + 1 \|I - 3I + 1 + (- I + I)\|- I \|- I + 1 ) ---R * ---R +----------+ ---R | 2 ---R \|I + I + 1 ---R + ---R +-----------+ ---R 2 +---+ +-------+ | 2 3 +---+ +-------+ ---R (- I - I)\|- I \|- I + 1 \|I - 3I + 1 + (I - I)\|- I \|- I + 1 ---R * ---R log ---R +----------+ ---R 2 +---+ 3 2 | 2 ---R ((- 4I - 6I - 4)\|- I + 2I + 2I + 2I + 2)\|I + I + 1 ---R + ---R 3 2 +---+ 4 3 2 ---R (4I + 8I + 8I + 4)\|- I - 2I - 3I - 4I - 3I - 2 ---R / ---R +----------+ ---R 3 2 | 2 4 3 2 ---R (2I + 6I + 6I + 2)\|I + I + 1 - 2I - 7I - 10I - 7I - 2 ---R + ---R +-----------+ +----------+ ---R 2 | 2 3 2 | 2 ---R (- I \|I - 3I + 1 + I - I )\|I + I + 1 ---R + ---R +-----------+ ---R 3 2 | 2 4 2 ---R (I + I )\|I - 3I + 1 - I + I ---R * ---R log ---R 3 2 +-------+ 4 3 2 ---R ((- 4I + 8I - 6I + 2)\|- I + 1 - 2I + 8I - 10I + 4I) ---R * ---R +-----------+ ---R | 2 ---R \|I - 3I + 1 ---R + ---R 4 3 2 +-------+ 5 4 3 2 ---R (4I - 14I + 14I - 4I)\|- I + 1 + 2I - 11I + 21I - 20I ---R + ---R 10I - 2 ---R / ---R +-----------+ ---R | 2 2 ---R (2I - 2)\|I - 3I + 1 - 2I + 5I - 2 ---R + ---R +-----------+ +----------+ ---R +-------+ | 2 +-------+ | 2 ---R (- 4\|- I + 1 \|I - 3I + 1 + (6I - 4)\|- I + 1 )\|I + I + 1 ---R + ---R +-----------+ ---R +-------+ | 2 2 +-------+ ---R (2I + 4)\|- I + 1 \|I - 3I + 1 + (- 4I - 4I + 4)\|- I + 1 ---R / ---R +-----------+ +----------+ ---R +-------+ | 2 +-------+ | 2 ---R (2\|- I + 1 \|I - 3I + 1 + (- 2I + 2)\|- I + 1 )\|I + I + 1 ---R + ---R +-----------+ ---R +-------+ | 2 2 +-------+ ---R (- 2I - 2)\|- I + 1 \|I - 3I + 1 + (2I - 2)\|- I + 1 ---R , ---R ---R +-----------+ ---R +---+ +-----+ | 2 2 +---+ +-----+ ---R (- I\|- I \|I - 1 \|I - 3I + 1 + (I - I)\|- I \|I - 1 ) ---R * ---R +----------+ ---R | 2 ---R \|I + I + 1 ---R + ---R +-----------+ ---R 2 +---+ +-----+ | 2 3 +---+ +-----+ ---R (I + I)\|- I \|I - 1 \|I - 3I + 1 + (- I + I)\|- I \|I - 1 ---R * ---R log ---R +-----------+ ---R 2 +---+ 3 2 | 2 ---R ((4I - 10I + 4)\|- I + 2I - 10I + 10I - 2)\|I - 3I + 1 ---R + ---R 3 2 +---+ 4 3 2 ---R (- 4I + 16I - 16I + 4)\|- I - 2I + 13I - 24I + 13I - 2 ---R / ---R +-----------+ ---R 3 2 | 2 4 3 2 ---R (2I - 6I + 6I - 2)\|I - 3I + 1 - 2I + 9I - 14I + 9I - 2 ---R + ---R +-----------+ ---R +---+ +-----+ | 2 2 +---+ +-----+ ---R (I\|- I \|I - 1 \|I - 3I + 1 + (- I + I)\|- I \|I - 1 ) ---R * ---R +----------+ ---R | 2 ---R \|I + I + 1 ---R + ---R +-----------+ ---R 2 +---+ +-----+ | 2 3 +---+ +-----+ ---R (- I - I)\|- I \|I - 1 \|I - 3I + 1 + (I - I)\|- I \|I - 1 ---R * ---R log ---R +----------+ ---R 2 +---+ 3 2 | 2 ---R ((- 4I - 6I - 4)\|- I + 2I + 2I + 2I + 2)\|I + I + 1 ---R + ---R 3 2 +---+ 4 3 2 ---R (4I + 8I + 8I + 4)\|- I - 2I - 3I - 4I - 3I - 2 ---R / ---R +----------+ ---R 3 2 | 2 4 3 2 ---R (2I + 6I + 6I + 2)\|I + I + 1 - 2I - 7I - 10I - 7I - 2 ---R + ---R +-----------+ +----------+ ---R 2 | 2 3 2 | 2 ---R (- 4I \|I - 3I + 1 + 4I - 4I )\|I + I + 1 ---R + ---R +-----------+ ---R 3 2 | 2 4 2 ---R (4I + 4I )\|I - 3I + 1 - 4I + 4I ---R * ---R +----------+ ---R +-----+ | 2 +-----+ ---R \|I - 1 \|I + I + 1 - I\|I - 1 ---R atan(---------------------------------) ---R I - 1 ---R + ---R +-----------+ +----------+ ---R 2 | 2 3 2 | 2 ---R (- 4I \|I - 3I + 1 + 4I - 4I )\|I + I + 1 ---R + ---R +-----------+ ---R 3 2 | 2 4 2 ---R (4I + 4I )\|I - 3I + 1 - 4I + 4I ---R * ---R +-----------+ ---R +-----+ | 2 +-----+ ---R \|I - 1 \|I - 3I + 1 - I\|I - 1 ---R atan(----------------------------------) ---R I - 1 ---R + ---R +-----------+ +----------+ ---R +-----+ | 2 +-----+ | 2 ---R (- 4\|I - 1 \|I - 3I + 1 + (6I - 4)\|I - 1 )\|I + I + 1 ---R + ---R +-----------+ ---R +-----+ | 2 2 +-----+ ---R (2I + 4)\|I - 1 \|I - 3I + 1 + (- 4I - 4I + 4)\|I - 1 ---R / ---R +-----------+ +----------+ ---R +-----+ | 2 +-----+ | 2 ---R (2\|I - 1 \|I - 3I + 1 + (- 2I + 2)\|I - 1 )\|I + I + 1 ---R + ---R +-----------+ ---R +-----+ | 2 2 +-----+ ---R (- 2I - 2)\|I - 1 \|I - 3I + 1 + (2I - 2)\|I - 1 ---R , ---R ---R +-----------+ +----------+ ---R 2 | 2 3 2 | 2 ---R (I \|I - 3I + 1 - I + I )\|I + I + 1 ---R + ---R +-----------+ ---R 3 2 | 2 4 2 ---R (- I - I )\|I - 3I + 1 + I - I ---R * ---R log ---R 3 2 +-------+ 4 3 2 ---R ((4I - 4I + 2I - 2)\|- I + 1 - 2I + 4I - 6I + 4I) ---R * ---R +----------+ ---R | 2 ---R \|I + I + 1 ---R + ---R 4 3 2 +-------+ 5 4 3 2 ---R (- 4I + 2I - 2I + 4I)\|- I + 1 + 2I - 3I + 5I - 4I ---R + ---R 2I - 2 ---R / ---R +----------+ ---R | 2 2 ---R (2I + 2)\|I + I + 1 - 2I - 3I - 2 ---R + ---R +-----------+ +----------+ ---R 2 | 2 3 2 | 2 ---R (- I \|I - 3I + 1 + I - I )\|I + I + 1 ---R + ---R +-----------+ ---R 3 2 | 2 4 2 ---R (I + I )\|I - 3I + 1 - I + I ---R * ---R log ---R 3 2 +-------+ 4 3 2 ---R ((- 4I + 8I - 6I + 2)\|- I + 1 - 2I + 8I - 10I + 4I) ---R * ---R +-----------+ ---R | 2 ---R \|I - 3I + 1 ---R + ---R 4 3 2 +-------+ 5 4 3 2 ---R (4I - 14I + 14I - 4I)\|- I + 1 + 2I - 11I + 21I - 20I ---R + ---R 10I - 2 ---R / ---R +-----------+ ---R | 2 2 ---R (2I - 2)\|I - 3I + 1 - 2I + 5I - 2 ---R + ---R +-----------+ ---R +-------+ +-+ | 2 2 +-------+ +-+ ---R (- 4I\|- I + 1 \|I \|I - 3I + 1 + (4I - 4I)\|- I + 1 \|I ) ---R * ---R +----------+ ---R | 2 ---R \|I + I + 1 ---R + ---R +-----------+ ---R 2 +-------+ +-+ | 2 3 +-------+ +-+ ---R (4I + 4I)\|- I + 1 \|I \|I - 3I + 1 + (- 4I + 4I)\|- I + 1 \|I ---R * ---R +-+ ---R \|I ---R atan(----------------------) ---R +-----------+ ---R | 2 ---R \|I - 3I + 1 - I + 1 ---R + ---R +-----------+ ---R +-------+ +-+ | 2 2 +-------+ +-+ ---R (- 4I\|- I + 1 \|I \|I - 3I + 1 + (4I - 4I)\|- I + 1 \|I ) ---R * ---R +----------+ ---R | 2 ---R \|I + I + 1 ---R + ---R +-----------+ ---R 2 +-------+ +-+ | 2 3 +-------+ +-+ ---R (4I + 4I)\|- I + 1 \|I \|I - 3I + 1 + (- 4I + 4I)\|- I + 1 \|I ---R * ---R +-+ ---R \|I ---R atan(---------------------) ---R +----------+ ---R | 2 ---R \|I + I + 1 - I - 1 ---R + ---R +-----------+ +----------+ ---R +-------+ | 2 +-------+ | 2 ---R (- 4\|- I + 1 \|I - 3I + 1 + (6I - 4)\|- I + 1 )\|I + I + 1 ---R + ---R +-----------+ ---R +-------+ | 2 2 +-------+ ---R (2I + 4)\|- I + 1 \|I - 3I + 1 + (- 4I - 4I + 4)\|- I + 1 ---R / ---R +-----------+ +----------+ ---R +-------+ | 2 +-------+ | 2 ---R (2\|- I + 1 \|I - 3I + 1 + (- 2I + 2)\|- I + 1 )\|I + I + 1 ---R + ---R +-----------+ ---R +-------+ | 2 2 +-------+ ---R (- 2I - 2)\|- I + 1 \|I - 3I + 1 + (2I - 2)\|- I + 1 ---R , ---R ---R +-----------+ +----------+ ---R 2 | 2 3 2 | 2 ---R (- 2I \|I - 3I + 1 + 2I - 2I )\|I + I + 1 ---R + ---R +-----------+ ---R 3 2 | 2 4 2 ---R (2I + 2I )\|I - 3I + 1 - 2I + 2I ---R * ---R +----------+ ---R +-----+ | 2 +-----+ ---R \|I - 1 \|I + I + 1 - I\|I - 1 ---R atan(---------------------------------) ---R I - 1 ---R + ---R +-----------+ +----------+ ---R 2 | 2 3 2 | 2 ---R (- 2I \|I - 3I + 1 + 2I - 2I )\|I + I + 1 ---R + ---R +-----------+ ---R 3 2 | 2 4 2 ---R (2I + 2I )\|I - 3I + 1 - 2I + 2I ---R * ---R +-----------+ ---R +-----+ | 2 +-----+ ---R \|I - 1 \|I - 3I + 1 - I\|I - 1 ---R atan(----------------------------------) ---R I - 1 ---R + ---R +-----------+ ---R +-----+ +-+ | 2 2 +-----+ +-+ ---R (- 2I\|I - 1 \|I \|I - 3I + 1 + (2I - 2I)\|I - 1 \|I ) ---R * ---R +----------+ ---R | 2 ---R \|I + I + 1 ---R + ---R +-----------+ ---R 2 +-----+ +-+ | 2 3 +-----+ +-+ ---R (2I + 2I)\|I - 1 \|I \|I - 3I + 1 + (- 2I + 2I)\|I - 1 \|I ---R * ---R +-+ ---R \|I ---R atan(----------------------) ---R +-----------+ ---R | 2 ---R \|I - 3I + 1 - I + 1 ---R + ---R +-----------+ ---R +-----+ +-+ | 2 2 +-----+ +-+ ---R (- 2I\|I - 1 \|I \|I - 3I + 1 + (2I - 2I)\|I - 1 \|I ) ---R * ---R +----------+ ---R | 2 ---R \|I + I + 1 ---R + ---R +-----------+ ---R 2 +-----+ +-+ | 2 3 +-----+ +-+ ---R (2I + 2I)\|I - 1 \|I \|I - 3I + 1 + (- 2I + 2I)\|I - 1 \|I ---R * ---R +-+ ---R \|I ---R atan(---------------------) ---R +----------+ ---R | 2 ---R \|I + I + 1 - I - 1 ---R + ---R +-----------+ +----------+ ---R +-----+ | 2 +-----+ | 2 ---R (- 2\|I - 1 \|I - 3I + 1 + (3I - 2)\|I - 1 )\|I + I + 1 ---R + ---R +-----------+ ---R +-----+ | 2 2 +-----+ ---R (I + 2)\|I - 1 \|I - 3I + 1 + (- 2I - 2I + 2)\|I - 1 ---R / ---R +-----------+ +----------+ ---R +-----+ | 2 +-----+ | 2 ---R (\|I - 1 \|I - 3I + 1 + (- I + 1)\|I - 1 )\|I + I + 1 ---R + ---R +-----------+ ---R +-----+ | 2 2 +-----+ ---R (- I - 1)\|I - 1 \|I - 3I + 1 + (I - 1)\|I - 1 ---R ] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 161 - ---S 162 of 267 -in2109a:=integrate((1+I*z)^(1/2)+cot(z-1), z= 0..1,"noPole") ---R ---R ---R (160) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 162 +--E 132 ---S 163 of 267 +--S 133 of 224 in2112a:=integrate(-cot(z-1)+log(1-1/z^4), z= -1..1,"noPole") --R --R ---R (161) + infinity +--R (133) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 163 +--E 133 ---S 164 of 267 +--S 134 of 224 in2115a:=integrate(-z/(z-1)+log(1-z^(1/3)), z= -1..1,"noPole") --R --R ---R (162) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 164 - ---S 165 of 267 -in2120a:=integrate(-z+1/(z^2+I*z-3)^(1/2), z= -1..1,"noPole") ---R ---R ---R (163) ---R +-------+ 2 ---R log((- 4I + 8)\|- I - 2 + I - 8I - 4) ---R + ---R +-----+ 2 ---R - log((- 4I - 8)\|I - 2 + I + 8I - 4) ---R / ---R 2 +--R (134) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 165 +--E 134 ---S 166 of 267 -in2124a:=integrate(-1/z-1/(I/(z+I))^(1/2), z= -1..0,"noPole") +--S 135 of 224 +in2120a:=integrate(-z+1/(z^2+%i*z-3)^(1/2), z= -1..1,"noPole") --R --R ---R (164) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 166 +--R (135) +--R +--------+ +--------+ +--R log((8 - 4%i)\|- 2 - %i - 5 - 8%i) - log((- 8 - 4%i)\|- 2 + %i - 5 + 8%i) +--R --------------------------------------------------------------------------- +--R 2 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 135 ---S 167 of 267 -in25:=integrate(cos(z), z= I..a) +--S 136 of 224 +in25:=integrate(cos(z), z= %i..a) --R --R ---R (165) sin(a) - sin(I) ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 167 +--R (136) sin(a) - sin(%i) +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 136 ---S 168 of 267 +--S 137 of 224 in25a:=integrate(cos(z), z= %i..a) --R --R ---R (166) sin(a) - sin(%i) +--R (137) sin(a) - sin(%i) --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 168 +--E 137 ---S 169 of 267 -in25b:=integrate(exp(I*z), z= I..I*infinity) +--S 138 of 224 +in25b:=integrate(exp(%i*z), z= %i..%i*infinity) --R --R ---R 2 2 ---R I infinity I ---R %e - %e ---R (167) ------------------- ---R I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 169 +--R - infinity +--R - %i %e %e + %i +--R (138) ------------------------- +--R %e +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 138 ---S 170 of 267 -in25c:=integrate(exp(%i*z), z= %i..I*infinity) +--S 139 of 224 +in25c:=integrate(exp(%i*z), z= %i..%i*infinity) --R --R ---R %i I infinity ---R - %i %e %e + %i ---R (168) ---------------------------- ---R %e +--R - infinity +--R - %i %e %e + %i +--R (139) ------------------------- +--R %e --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 170 +--E 139 ---S 171 of 267 +--S 140 of 224 in28a:=integrate(1/z, z=1..z,"noPole") --R --R --R 2 --R log(z ) ---R (169) ------- +--R (140) ------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 171 +--E 140 ---S 172 of 267 +--S 141 of 224 in30:=integrate(sin(3*asin(1/(1+z^2))), z= 0..%plusInfinity) --R --R --R 3%pi ---R (170) ---- +--R (141) ---- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 172 +--E 141 ---S 173 of 267 +--S 142 of 224 in32:=integrate(exp(-z), z= 0..%plusInfinity) --R --R ---R (171) 1 +--R (142) 1 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 173 +--E 142 ---S 174 of 267 +--S 143 of 224 in34a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole") --R --R ---R (172) +--R (143) --R log --R 2 2 --R - 12sin(1) + (42cos(1) + 48)sin(1) - 36cos(1) - 84cos(1) @@ -4776,315 +4423,202 @@ in34a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole") --R +-+ --R \|3 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 174 +--E 143 ---S 175 of 267 +--S 144 of 224 in37:=integrate(atan(tan(1/z)), z= 0..1) --R --R ---R (173) + infinity +--R (144) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 175 +--E 144 ---S 176 of 267 +--S 145 of 224 in40:=integrate(atan(tan(z)), z= 0..%plusInfinity) --R --R ---R (174) + infinity +--R (145) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 176 +--E 145 ---S 177 of 267 +--S 146 of 224 in2157a:=integrate(acoth(z)-1/(1+z^(1/2)), z= 0..1,"noPole") --R --R --R log(4) + 10log(2) - 8 ---R (175) --------------------- +--R (146) --------------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 177 +--E 146 ---S 178 of 267 +--S 147 of 224 in2158a:=integrate(2*acoth(1-(1-z)^(1/2)), z= 0..1,"noPole") --R --R ---R (176) 2log(4) - 2 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 178 - ---S 179 of 267 -in2168a:=integrate(-csch(z-1)-(1+I*z)^(1/2), z= 0..1,"noPole") ---R ---R ---R (177) + infinity +--R (147) 2log(4) - 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 179 +--E 147 ---S 180 of 267 -in2179a:=integrate((z^3-I*(1-z^4)^(1/2))^4, z= -1..1,"noPole") +--S 148 of 224 +in2168a:=integrate(-csch(z-1)-(1+%i*z)^(1/2), z= 0..1,"noPole") --R --R ---R 4 2 ---R 64064I + 28080I + 6930 ---R (178) ------------------------ ---R 45045 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 180 +--R (148) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 148 ---S 181 of 267 -in2185a:=integrate(csch(z)+(z^2-I*z+1)^(1/2), z= 0..1,"noPole") +--S 149 of 224 +in2185a:=integrate(csch(z)+(z^2-%i*z+1)^(1/2), z= 0..1,"noPole") --R --R ---R (179) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 181 +--R (149) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 149 ---S 182 of 267 +--S 150 of 224 in2195a:=integrate(1-acoth(1-(1-z)^(1/2)), z= -1..1,"noPole") --R --R ---R (180) +--R (150) --R +-+ +-+ +-+ +-+ --R 2log(\|2 ) - log(- 2\|2 + 3) + 3log(- 4\|2 + 6) + 4\|2 - 4log(4) + 8 --R ----------------------------------------------------------------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 182 +--E 150 ---S 183 of 267 +--S 151 of 224 in2201a:=integrate(acoth(z)+%pi-asec(z-1), z= 0..1,"noPole") --R --R --R +-+ --R - %pi\|2 + log(4) + 2%pi ---R (181) ------------------------- +--R (151) ------------------------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 183 +--E 151 ---S 184 of 267 +--S 152 of 224 in221:=integrate(log(z+sqrt(z^2-1)), z) --R --R --R +------+ +------+ +------+ --R | 2 2 | 2 | 2 2 --R (z\|z - 1 - z )log(\|z - 1 + z) + z\|z - 1 - z + 1 ---R (182) --------------------------------------------------------- +--R (152) --------------------------------------------------------- --R +------+ --R | 2 --R \|z - 1 - z --R Type: Union(Expression Integer,...) ---E 184 +--E 152 ---S 185 of 267 +--S 153 of 224 in227a:=integrate(atan(sin(z))+atan(1/(sin(z))), z= 0..1,"noPole") --R --R --R %pi ---R (183) - --- +--R (153) - --- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 185 +--E 153 ---S 186 of 267 +--S 154 of 224 in237a:=integrate(sin(z)*(1-cos(z)/sqrt(1-sin(z)^2))^2, z= 0..1,"noPole") --R --R ---R (184) - 4cos(1) + 4 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 186 - ---S 187 of 267 -in2221:=integrate((z-I)*(-1+1/(z-I)), z= 0..%plusInfinity) ---R ---R ---R (185) - infinity +--R (154) - 4cos(1) + 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 187 +--E 154 ---S 188 of 267 -in2243a:=integrate(-1/sinh(z-1)+1/(I*z)^(1/2), z= 0..1,"noPole") +--S 155 of 224 +in2221:=integrate((z-%i)*(-1+1/(z-%i)), z= 0..%plusInfinity) --R --R ---R (186) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 188 +--R (155) - infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 155 ---S 189 of 267 -in2247a:=integrate(1/(z^2-I*z+2)^(1/2)+csc(z), z= 0..1,"noPole") +--S 156 of 224 +in2243a:=integrate(-1/sinh(z-1)+1/(%i*z)^(1/2), z= 0..1,"noPole") --R --R ---R (187) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 189 +--R (156) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 156 ---S 190 of 267 +--S 157 of 224 in2254a:=integrate(cosh(z^(1/2))-acoth(1-z), z= 0..1,"noPole") --R --R --R - %e log(4) + 4%e - 4 ---R (188) --------------------- +--R (157) --------------------- --R 2%e --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 190 +--E 157 ---S 191 of 267 -in2270a:=integrate(log(z)*log(1/z)*(I*z)^(1/3), z= -1..1,"noPole") +--S 158 of 224 +in2270a:=integrate(log(z)*log(1/z)*(%i*z)^(1/3), z= -1..1,"noPole") --R --R ---R 3+-+ 3+---+ ---R - 27\|I - 27\|- I ---R (189) ------------------- ---R 32 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 191 +--R 3+--+ 3+----+ +--R - 27\|%i - 27\|- %i +--R (158) --------------------- +--R 32 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 158 ---S 192 of 267 +--S 159 of 224 in2274a:=integrate(acoth(1-z)-acosh(1/z), z= -1..1,"noPole") --R --R --R 3log(9) - 4%pi ---R (190) -------------- +--R (159) -------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 192 +--E 159 ---S 193 of 267 -in2275a:=integrate((z^2+I*z-3)^(1/2)*(3+z^2), z= -1..1,"noPole") +--S 160 of 224 +in2275a:=integrate((z^2+%i*z-3)^(1/2)*(3+z^2), z= -1..1,"noPole") --R --R ---R (191) ---R 10 8 6 4 2 ---R - 960I + 49920I + 1320960I + 3563520I - 40550400I ---R + ---R 8847360 ---R * ---R +-------+ ---R \|- I - 2 ---R + ---R 11 10 9 8 7 6 ---R 120I - 2640I - 23520I + 10560I - 318720I + 1359360I ---R + ---R 5 4 3 2 ---R 3056640I + 9922560I + 36034560I - 2396160I - 40919040I ---R + ---R 15482880 ---R * ---R +-----+ ---R \|I - 2 +--R (160) +--R +--------+ +--------+ +--R (- 51691200\|- 2 - %i - 26455440 + 73601880%i)\|- 2 + %i --R + ---R 11 10 9 8 7 6 ---R 120I + 2640I - 23520I - 10560I - 318720I - 1359360I ---R + ---R 5 4 3 2 ---R 3056640I - 9922560I + 36034560I + 2396160I - 40919040I ---R + ---R - 15482880 ---R * ---R +-------+ ---R \|- I - 2 ---R + ---R 12 10 8 6 4 2 ---R - 15I + 12360I + 67440I - 3283200I - 21131520I + 73451520I ---R + ---R - 27095040 +--R +--------+ +--R (26455440 + 73601880%i)\|- 2 - %i + 118339815 --R * ---R +-------+ 2 ---R log((- 4I + 8)\|- I - 2 + I - 8I - 4) +--R +--------+ +--R log((8 - 4%i)\|- 2 - %i - 5 - 8%i) --R + ---R 10 8 6 4 2 ---R 960I - 49920I - 1320960I - 3563520I + 40550400I ---R + ---R - 8847360 ---R * ---R +-------+ ---R \|- I - 2 ---R + ---R 11 10 9 8 7 6 ---R - 120I + 2640I + 23520I - 10560I + 318720I - 1359360I ---R + ---R 5 4 3 2 ---R - 3056640I - 9922560I - 36034560I + 2396160I + 40919040I ---R + ---R - 15482880 ---R * ---R +-----+ ---R \|I - 2 ---R + ---R 11 10 9 8 7 6 ---R - 120I - 2640I + 23520I + 10560I + 318720I + 1359360I ---R + ---R 5 4 3 2 ---R - 3056640I + 9922560I - 36034560I - 2396160I + 40919040I ---R + ---R 15482880 ---R * ---R +-------+ ---R \|- I - 2 ---R + ---R 12 10 8 6 4 2 ---R 15I - 12360I - 67440I + 3283200I + 21131520I - 73451520I +--R +--------+ +--------+ +--R (51691200\|- 2 - %i + 26455440 - 73601880%i)\|- 2 + %i --R + ---R 27095040 +--R +--------+ +--R (- 26455440 - 73601880%i)\|- 2 - %i - 118339815 --R * ---R +-----+ 2 ---R log((- 4I - 8)\|I - 2 + I + 8I - 4) +--R +--------+ +--R log((- 8 - 4%i)\|- 2 + %i - 5 + 8%i) --R + ---R 9 5 3 +-------+ 11 ---R (- 20480I + 17170432I - 48234496I + 57671680I)\|- I - 2 + 60I ---R + ---R 10 9 8 7 6 5 ---R 3800I - 39408I - 172896I - 790144I - 6873344I + 13455872I ---R + ---R 4 3 2 ---R 53588992I - 16978944I - 85084160I + 9687040I + 21897216 ---R * ---R +-----+ ---R \|I - 2 +--R +--------+ +--------+ +--R (- 123056128%i\|- 2 - %i - 167267016 - 40872532%i)\|- 2 + %i --R + ---R 11 10 9 8 7 6 ---R - 60I + 3800I + 39408I - 172896I + 790144I - 6873344I ---R + ---R 5 4 3 2 ---R - 13455872I + 53588992I + 16978944I - 85084160I - 9687040I ---R + ---R 21897216 ---R * ---R +-------+ ---R \|- I - 2 ---R + ---R 11 9 7 5 3 ---R - 960I + 133888I + 3352576I - 44081152I + 129318912I - 59834368I +--R +--------+ +--R (- 167267016 + 40872532%i)\|- 2 - %i + 236452160%i --R / ---R 6 4 2 +-------+ 7 ---R (49152I - 3735552I + 14942208I - 3145728)\|- I - 2 - 6144I ---R + ---R 6 5 4 3 2 ---R 135168I + 1351680I - 3784704I - 15237120I + 1769472I + 14548992I ---R + ---R - 5505024 ---R * ---R +-----+ ---R \|I - 2 +--R +--------+ +--------+ +--R (21872640\|- 2 - %i + 11194368 - 31143936%i)\|- 2 + %i --R + ---R 7 6 5 4 3 2 ---R - 6144I - 135168I + 1351680I + 3784704I - 15237120I - 1769472I ---R + ---R 14548992I + 5505024 ---R * ---R +-------+ ---R \|- I - 2 ---R + ---R 8 6 4 2 ---R 768I - 651264I + 12066816I - 27721728I + 9633792 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 193 +--R +--------+ +--R (- 11194368 - 31143936%i)\|- 2 - %i - 50074368 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 160 ---S 194 of 267 +--S 161 of 224 in2276a:=integrate((1-tanh(log(1+z^(1/3))))^5, z= -1..1,"noPole") --R --R ---R (192) +--R (161) --R 3+---+2 3+---+ 3+---+ --R (- 918750\|- 1 + 1200000\|- 1 + 2100000)atan(\|- 1 + 1) --R + @@ -5096,23 +4630,23 @@ in2276a:=integrate((1-tanh(log(1+z^(1/3))))^5, z= -1..1,"noPole") --R 3+---+2 3+---+ --R 30625\|- 1 - 40000\|- 1 - 70000 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 194 +--E 161 ---S 195 of 267 +--S 162 of 224 in2278a:=integrate(acoth(1-z)+log(abs(z-1)/z), z= 0..1,"noPole") --R --R --R log(4) ---R (193) ------ +--R (162) ------ --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 195 +--E 162 ---S 196 of 267 +--S 163 of 224 in2279a:=integrate(acoth(1/(z^2-z+1)^(1/2)), z= -1..1,"noPole") --R --R ---R (194) +--R (163) --R +-+ --R +-+ +-+ +-+ - \|3 - 2 --R 2log(12\|3 + 21) + log(6\|3 + 12) - log(2\|3 + 4) + log(----------) @@ -5123,184 +4657,148 @@ in2279a:=integrate(acoth(1/(z^2-z+1)^(1/2)), z= -1..1,"noPole") --R / --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 196 +--E 163 ---S 197 of 267 -in2307a:=integrate(tan(z)-1/(z^2+I*z-3)^(1/2), z= -1..1,"noPole") +--S 164 of 224 +in2311a:=integrate(-1/sinh(z-1)+1/(%i*z)^(1/2), z= 0..%pi,"noPole") --R --R ---R (195) ---R +-------+ 2 ---R - log((- 4I + 8)\|- I - 2 + I - 8I - 4) +--R (164) +--R %pi - 1 2 %pi - 1 %pi - 1 2 %pi - 1 +--R log((%e ) + 2%e + 1) - log((%e ) - 2%e + 1) --R + ---R +-----+ 2 ---R log((- 4I - 8)\|I - 2 + I + 8I - 4) +--R 2 2 +--R +------+ %e + 2%e + 1 %e - 2%e + 1 +--R - 4%i\|%i %pi - log(-------------) + log(-------------) +--R 2 2 +--R %e %e --R / --R 2 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 197 - ---S 198 of 267 -in2311a:=integrate(-1/sinh(z-1)+1/(I*z)^(1/2), z= 0..%pi,"noPole") ---R ---R ---R (196) ---R %pi - 1 2 %pi - 1 ---R I log((%e ) + 2%e + 1) ---R + ---R 2 ---R %pi - 1 2 %pi - 1 +-----+ %e + 2%e + 1 ---R - I log((%e ) - 2%e + 1) + 4\|I %pi - I log(-------------) ---R 2 ---R %e ---R + ---R 2 ---R %e - 2%e + 1 ---R I log(-------------) ---R 2 ---R %e ---R / ---R 2I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 198 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 164 ---S 199 of 267 -in2312:=integrate(sin(z)-1/(z^2+I*z-1)^(1/2), z= -1..1) +--S 165 of 224 +in2312:=integrate(sin(z)-1/(z^2+%i*z-1)^(1/2), z= -1..1) --R --R ---R (197) potentialPole +--R (165) potentialPole --R Type: Union(pole: potentialPole,...) ---E 199 +--E 165 ---S 200 of 267 -in2312a:=integrate(sin(z)-1/(z^2+I*z-1)^(1/2), z= -1..1,"noPole") +--S 166 of 224 +in2312a:=integrate(sin(z)-1/(z^2+%i*z-1)^(1/2), z= -1..1,"noPole") --R --R ---R (198) ---R +---+ 2 +-+ 2 ---R - log((- 4I + 8)\|- I + I - 8I + 4) + log((- 4I - 8)\|I + I + 8I + 4) ---R ------------------------------------------------------------------------- ---R 2 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 200 +--R +----+ +--+ +--R - log((8 - 4%i)\|- %i + 3 - 8%i) + log((- 8 - 4%i)\|%i + 3 + 8%i) +--R (166) ------------------------------------------------------------------- +--R 2 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 166 ---S 201 of 267 +--S 167 of 224 in2324a:=integrate(cosh(z^(1/2)-1)+acoth(1-z), z= 0..1,"noPole") --R --R --R 2 --R %e log(4) + 2%e - 4%e + 2 ---R (199) -------------------------- +--R (167) -------------------------- --R 2%e --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 201 +--E 167 ---S 202 of 267 -in2330a:=integrate(exp(-z)+1/(z^2+I*z-1)^(1/2), z= -1..1,"noPole") +--S 168 of 224 +in2330a:=integrate(exp(-z)+1/(z^2+%i*z-1)^(1/2), z= -1..1,"noPole") --R --R ---R (200) ---R +---+ 2 ---R %e log((- 4I + 8)\|- I + I - 8I + 4) +--R (168) +--R +----+ +--+ +--R %e log((8 - 4%i)\|- %i + 3 - 8%i) - %e log((- 8 - 4%i)\|%i + 3 + 8%i) --R + ---R +-+ 2 2 ---R - %e log((- 4I - 8)\|I + I + 8I + 4) + 2%e - 2 +--R 2 +--R 2%e - 2 --R / --R 2%e ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 202 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 168 ---S 203 of 267 +--S 169 of 224 in2332a:=integrate(acoth(z^(1/2))*(1-z^(1/2)), z= 0..1,"noPole") --R --R --R log(16) - log(4) - 10log(2) + 8 ---R (201) ------------------------------- +--R (169) ------------------------------- --R 12 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 203 +--E 169 ---S 204 of 267 +--S 170 of 224 in2333a:=integrate(acoth(z)+1/(z^2+z+2)^(1/2), z= 0..1,"noPole") --R --R --R +-+ --R log(- 4\|2 + 9) + log(4) ---R (202) ------------------------- +--R (170) ------------------------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 204 - ---S 205 of 267 -in2340a:=integrate(exp(I*(I*z)^(1/2))+cot(z-1), z= -1..1,"noPole") ---R ---R ---R (203) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 205 +--E 170 ---S 206 of 267 -in2360a:=integrate(1/(1-I*z^2)^(1/2)-csch(z-1), z= -1..1,"noPole") +--S 171 of 224 +in2360a:=integrate(1/(1-%i*z^2)^(1/2)-csch(z-1), z= -1..1,"noPole") --R --R ---R (204) [ + infinity, + infinity] ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 206 +--R (171) [ + infinity, + infinity] +--R Type: Union(f2: List OrderedCompletion Expression Complex Integer,...) +--E 171 ---S 207 of 267 -in2367a:=integrate(log(1-z^2)-1/(I/(z-I))^(1/2), z= -1..1,"noPole") +--S 172 of 224 +in2367a:=integrate(log(1-z^2)-1/(%i/(z-%i))^(1/2), z= -1..1,"noPole") --R --R ---R (205) ---R 4 4 1 ---R 3log(-----------) + 3log(-----------) - 3log(-----------) ---R 2 2 2 ---R I - 2I + 1 I + 2I + 1 I - 2I + 1 ---R + ---R 1 ---R - 3log(-----------) + 6log(4) - 24 ---R 2 ---R I + 2I + 1 +--R (172) +--R %i %i +--R (6log(4) + 3log(2%i) - 3log(--) - 3log(- --) + 3log(- 2%i) - 24) +--R 2 2 --R * ---R +-------+ ---R | I ---R |- ----- ---R \| I - 1 +--R +--------+ +--R | %i +--R |- ------ +--R \| 1 + %i --R + ---R 4I - 4 +--R - 4 - 4%i --R * ---R +-------+ ---R | I ---R |- ----- ---R \| I + 1 ---R + ---R +-------+ ---R | I ---R (- 4I - 4) |- ----- ---R \| I - 1 +--R +------+ +--R | 1 +--R |------ +--R \|1 + %i +--R + +--R +--------+ +--R | %i +--R (4 + 4%i) |- ------ +--R \| 1 + %i --R / ---R +-------+ +-------+ ---R | I | I ---R 6 |- ----- |- ----- ---R \| I - 1 \| I + 1 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 207 +--R +--------+ +------+ +--R | %i | 1 +--R 6 |- ------ |------ +--R \| 1 + %i \|1 + %i +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 172 ---S 208 of 267 +--S 173 of 224 in2375a:=integrate(acoth(1-z^(1/2))+1/z^(1/3), z= 0..1,"noPole") --R --R --R 2log(4) + 1 ---R (206) ----------- +--R (173) ----------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 208 +--E 173 ---S 209 of 267 +--S 174 of 224 in2376a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..infinity,"noPole") --R --R ---R (207) +--R (174) --R +-+ --R 3\|5 --R * @@ -5326,341 +4824,230 @@ in2376a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..infinity,"noPole") --R / --R 6 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 209 +--E 174 ---S 210 of 267 -in2378a:=integrate((z^2+I*z-3)^(1/2)-tanh(z-1), z= -1..1,"noPole") +--S 175 of 224 +in2378a:=integrate((z^2+%i*z-3)^(1/2)-tanh(z-1), z= -1..1,"noPole") --R --R ---R (208) ---R 4 2 +-------+ 5 4 3 2 ---R (- 16I - 128I + 768)\|- I - 2 + 4I - 24I - 32I - 320I ---R + ---R - 960I - 384 ---R * ---R +-----+ ---R \|I - 2 ---R + ---R 5 4 3 2 +-------+ 6 4 ---R (4I + 24I - 32I + 320I - 960I + 384)\|- I - 2 - I + 60I +--R (175) +--R +--------+ +--------+ +--R (- 880\|- 2 - %i + 88 + 924%i)\|- 2 + %i --R + ---R 2 ---R 848I - 192 +--R +--------+ +--R (- 88 + 924%i)\|- 2 - %i + 979 --R * ---R +-------+ 2 ---R log((- 4I + 8)\|- I - 2 + I - 8I - 4) +--R +--------+ +--R log((8 - 4%i)\|- 2 - %i - 5 - 8%i) --R + ---R 4 2 +-------+ 5 4 3 2 ---R (16I + 128I - 768)\|- I - 2 - 4I + 24I + 32I + 320I + 960I ---R + ---R 384 ---R * ---R +-----+ ---R \|I - 2 ---R + ---R 5 4 3 2 +-------+ 6 4 ---R (- 4I - 24I + 32I - 320I + 960I - 384)\|- I - 2 + I - 60I +--R +--------+ +--------+ +--------+ +--R (640\|- 2 - %i - 64 - 672%i)\|- 2 + %i + (64 - 672%i)\|- 2 - %i --R + ---R 2 ---R - 848I + 192 +--R - 712 --R * ---R +-----+ 2 ---R log((- 4I - 8)\|I - 2 + I + 8I - 4) ---R + ---R 2 4 2 2 ---R 2 (%e ) + 2(%e ) + 1 2 ---R (128I - 512)log(--------------------) + (- 128I + 512)log(4) ---R 2 4 ---R (%e ) ---R + ---R 3 2 ---R - 256I + 512I + 1024I - 2048 ---R * ---R +-------+ ---R \|- I - 2 +--R 2 4 2 2 +--R (%e ) + 2(%e ) + 1 +--R log(--------------------) +--R 2 4 +--R (%e ) +--R + +--R +--------+ +--------+ +--------+ +--R (880\|- 2 - %i - 88 - 924%i)\|- 2 + %i + (88 - 924%i)\|- 2 - %i --R + ---R 2 4 2 2 ---R 3 2 (%e ) + 2(%e ) + 1 ---R (- 32I + 192I + 640I + 256)log(--------------------) ---R 2 4 ---R (%e ) ---R + ---R 3 2 5 4 3 2 ---R (32I - 192I - 640I - 256)log(4) + 4I + 72I - 416I - 320I ---R + ---R 2624I + 2176 +--R - 979 --R * ---R +-----+ ---R \|I - 2 ---R + ---R 2 4 2 2 ---R 3 2 (%e ) + 2(%e ) + 1 ---R (- 32I - 192I + 640I - 256)log(--------------------) ---R 2 4 ---R (%e ) ---R + ---R 3 2 5 4 3 2 ---R (32I + 192I - 640I + 256)log(4) - 4I + 72I + 160I - 1856I +--R +--------+ +--R log((- 8 - 4%i)\|- 2 + %i - 5 + 8%i) +--R + +--R +--------+ +--R (- 640log(4) + 2560 - 1280%i)\|- 2 - %i + (64 + 672%i)log(4) - 2568 --R + ---R 2496I + 128 +--R - 3044%i --R * ---R +-------+ ---R \|- I - 2 +--R +--------+ +--R \|- 2 + %i --R + ---R 2 4 2 2 ---R 4 2 (%e ) + 2(%e ) + 1 ---R (8I - 576I + 128)log(--------------------) ---R 2 4 ---R (%e ) +--R +--------+ +--R ((- 64 + 672%i)log(4) - 2056 - 2332%i)\|- 2 - %i + 712log(4) - 2848 --R + ---R 4 2 5 4 3 2 ---R (- 8I + 576I - 128)log(4) - 32I + 32I + 768I - 2304I - 2560I + 512 +--R 3360%i --R / ---R 2 +-------+ 3 2 +-----+ ---R ((256I - 1024)\|- I - 2 - 64I + 384I + 1280I + 512)\|I - 2 +--R +--------+ +--------+ +--------+ +--R (1280\|- 2 - %i - 128 - 1344%i)\|- 2 + %i + (128 - 1344%i)\|- 2 - %i --R + ---R 3 2 +-------+ 4 2 ---R (- 64I - 384I + 1280I - 512)\|- I - 2 + 16I - 1152I + 256 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 210 +--R - 1424 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 175 ---S 211 of 267 +--S 176 of 224 in2386a:=integrate(acoth(1-z)-(z^2-z+2)^(1/2), z= 0..1,"noPole") --R --R --R +-+ +-+ +-+ --R - 7log(4\|2 + 9) + 7log(- 4\|2 + 9) - 8\|2 + 8log(4) ---R (209) ------------------------------------------------------- +--R (176) ------------------------------------------------------- --R 16 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 211 +--E 176 ---S 212 of 267 -in2390a:=integrate((z^2-I*z-2)^(1/2)+1/sec(z-1), z= -1..1,"noPole") +--S 177 of 224 +in2390a:=integrate((z^2-%i*z-2)^(1/2)+1/sec(z-1), z= -1..1,"noPole") --R --R ---R (210) ---R 8 6 4 2 +-------+ 9 8 ---R (- 64I + 3840I + 18432I - 131072I )\|- I - 1 - 8I + 176I ---R + ---R 7 6 5 4 3 2 ---R 1472I - 3456I - 1536I - 33792I - 102400I + 40960I + 65536I ---R * ---R +-----+ ---R \|I - 1 +--R (177) +--R 2%i +--------+ 2%i +--------+ +--R (- 560%e \|- 1 - %i + (168 - 476%i)%e )\|- 1 + %i --R + ---R 9 8 7 6 5 4 3 ---R - 8I - 176I + 1472I + 3456I - 1536I + 33792I - 102400I ---R + ---R 2 ---R - 40960I + 65536I ---R * ---R +-------+ ---R \|- I - 1 ---R + ---R 10 8 6 4 2 ---R - I + 792I - 6016I - 84992I + 110592I - 32768 +--R 2%i +--------+ 2%i +--R (- 168 - 476%i)%e \|- 1 - %i + 455%e --R * ---R +-----+ 2 ---R log((4I + 8)\|I - 1 + I + 8I) +--R +--------+ +--R log((8 + 4%i)\|- 1 + %i - 1 + 8%i) --R + ---R 8 6 4 2 +-------+ 9 8 ---R (64I - 3840I - 18432I + 131072I )\|- I - 1 + 8I - 176I ---R + ---R 7 6 5 4 3 2 ---R - 1472I + 3456I + 1536I + 33792I + 102400I - 40960I - 65536I ---R * ---R +-----+ ---R \|I - 1 ---R + ---R 9 8 7 6 5 4 3 ---R 8I + 176I - 1472I - 3456I + 1536I - 33792I + 102400I ---R + ---R 2 ---R 40960I - 65536I ---R * ---R +-------+ ---R \|- I - 1 ---R + ---R 10 8 6 4 2 ---R I - 792I + 6016I + 84992I - 110592I + 32768 ---R * ---R +-------+ 2 ---R log((4I - 8)\|- I - 1 + I - 8I) ---R + ---R 6 4 2 7 5 3 ---R (1024I - 69632I + 262144I )sin(2) + 1536I - 63488I + 262144I ---R + ---R - 131072I ---R * ---R +-------+ ---R \|- I - 1 ---R + ---R 7 6 5 4 3 2 ---R (128I - 2816I - 24576I + 77824I + 221184I - 81920I - 131072I) ---R * ---R sin(2) +--R 2%i +--------+ 2%i +--------+ +--R (560%e \|- 1 - %i + (- 168 + 476%i)%e )\|- 1 + %i --R + ---R 9 8 7 6 5 4 3 ---R 4I + 264I - 3456I - 24320I + 67072I + 199680I - 122880I ---R + ---R 2 ---R - 245760I + 16384I + 32768 +--R 2%i +--------+ 2%i +--R (168 + 476%i)%e \|- 1 - %i - 455%e --R * ---R +-----+ ---R \|I - 1 +--R +--------+ +--R log((- 8 + 4%i)\|- 1 - %i - 1 - 8%i) --R + ---R 7 6 5 4 3 2 ---R (128I + 2816I - 24576I - 77824I + 221184I + 81920I - 131072I) ---R * ---R sin(2) +--R 2%i 2 2%i +--------+ +--R (- 640%i (%e ) + 1280%i %e + 640%i)\|- 1 - %i --R + ---R 9 8 7 6 5 4 3 ---R - 4I + 264I + 3456I - 24320I - 67072I + 199680I + 122880I ---R + ---R 2 ---R - 245760I - 16384I + 32768 +--R 2%i 2 2%i +--R (544 + 192%i)(%e ) + (- 1480 - 580%i)%e - 544 - 192%i --R * ---R +-------+ ---R \|- I - 1 +--R +--------+ +--R \|- 1 + %i --R + ---R 8 6 4 2 9 7 ---R (16I - 12800I + 198656I - 229376I + 65536)sin(2) + 64I - 13824I +--R 2%i 2 2%i +--------+ +--R ((544 - 192%i)(%e ) + (- 1480 + 580%i)%e - 544 + 192%i)\|- 1 - %i --R + ---R 5 3 ---R 174080I - 327680I + 131072I +--R 2%i 2 2%i +--R 520%i (%e ) - 1824%i %e - 520%i --R / ---R 6 4 2 +-------+ 7 6 5 ---R (1024I - 69632I + 262144I )\|- I - 1 + 128I - 2816I - 24576I ---R + ---R 4 3 2 ---R 77824I + 221184I - 81920I - 131072I ---R * ---R +-----+ ---R \|I - 1 +--R 2%i +--------+ 2%i +--------+ +--R (1280%e \|- 1 - %i + (- 384 + 1088%i)%e )\|- 1 + %i --R + ---R 7 6 5 4 3 2 ---R (128I + 2816I - 24576I - 77824I + 221184I + 81920I - 131072I) ---R * ---R +-------+ ---R \|- I - 1 ---R + ---R 8 6 4 2 ---R 16I - 12800I + 198656I - 229376I + 65536 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 212 +--R 2%i +--------+ 2%i +--R (384 + 1088%i)%e \|- 1 - %i - 1040%e +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 177 ---S 213 of 267 +--S 178 of 224 in2392a:=integrate(1/sec(z-1)+acoth(1-z^(1/2)), z= 0..1,"noPole") --R --R ---R (211) sin(1) + log(4) - 1 +--R (178) sin(1) + log(4) - 1 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 213 +--E 178 ---S 214 of 267 -in2404a:=integrate(1/(1+I*z^2)^(1/2)+acoth(z), z= -1..1,"noPole") +--S 179 of 224 +in2404a:=integrate(1/(1+%i*z^2)^(1/2)+acoth(z), z= -1..1,"noPole") --R --R ---R (212) +--R (179) --R [ ---R - ---R log ---R 2 +-+ 2 +-----+ 2 +-+ 3 ---R ((2I + 4I)\|I + 4I + 2I)\|I + 1 + (- 4I - 4I)\|I - 2I ---R + ---R 2 ---R - 5I - 2I ---R / ---R +-----+ ---R 2\|I + 1 - I - 2 +--R +-----+ +--R \|- 4%i +--R * +--R log +--R +-----+ +------+ +-----+ +--R ((4 - 8%i)\|- 4%i + 8 + 16%i)\|1 + %i + (- 8 + 8%i)\|- 4%i +--R + +--R - 20%i +--R / +--R +------+ +--R 2\|1 + %i - 2 - %i --R + ---R log ---R 2 +-+ 2 +-----+ 2 +-+ 3 ---R ((- 2I - 4I)\|I + 4I + 2I)\|I + 1 + (4I + 4I)\|I - 2I ---R + ---R 2 ---R - 5I - 2I ---R / ---R +-----+ ---R 2\|I + 1 - I - 2 +--R - +--R +-----+ +--R \|- 4%i +--R * +--R log +--R +-----+ +------+ +--R ((- 4 + 8%i)\|- 4%i + 8 + 16%i)\|1 + %i +--R + +--R +-----+ +--R (8 - 8%i)\|- 4%i - 20%i +--R / +--R +------+ +--R 2\|1 + %i - 2 - %i --R / ---R +-+ ---R 2\|I +--R 4 --R , ---R +---+ +-----+ +---+ ---R \|- I \|I + 1 - \|- I ---R 4atan(-----------------------) ---R I ---R ------------------------------] ---R +---+ ---R \|- I ---R Type: Union(f2: List OrderedCompletion Expression Integer,...) ---E 214 +--R +------+ +--R +---+ 2%i\|1 + %i - 2%i +--R - 2\|4%i atan(------------------)] +--R +---+ +--R \|4%i +--R Type: Union(f2: List OrderedCompletion Expression Complex Integer,...) +--E 179 ---S 215 of 267 -in2409a:=integrate(tan(z)+1/(I/(z+I))^(1/2), z= 0..1/2*%pi,"noPole") +--S 180 of 224 +in2409a:=integrate(tan(z)+1/(%i/(z+%i))^(1/2), z= 0..1/2*%pi,"noPole") --R --R ---R (213) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 215 +--R (180) + infinity +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 180 ---S 216 of 267 -in248a:=integrate(log(z^I)^2, z= 0..1,"noPole") +--S 181 of 224 +in248a:=integrate(log(z^%i)^2, z= 0..1,"noPole") --R --R ---R 2 ---R (214) 2I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 216 +--R (181) - 2 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 181 ---S 217 of 267 +--S 182 of 224 in248b:=integrate(log(z^%i)^2, z= 0..1,"noPole") --R --R ---R (215) - 2 +--R (182) - 2 --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 217 +--E 182 ---S 218 of 267 +--S 183 of 224 in249a:=integrate((sin(z)/(cos(z)-1))^(1/3), z= 0..%pi,"noPole") --R --R --R 3+-+ 3+-+ +-+ --R 3log(32\|2 ) - 12log(2\|2 ) - 4%pi\|3 ---R (216) -------------------------------------- +--R (183) -------------------------------------- --R 24 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 218 +--E 183 ---S 219 of 267 +--S 184 of 224 in251a:=integrate((-1)^z*exp(-z)*sin(z), z= 0..%plusInfinity,"noPole") --R --R --R 2 --R - %pi + 2 ---R (217) ---------- +--R (184) ---------- --R 4 --R %pi + 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 219 +--E 184 ---S 220 of 267 +--S 185 of 224 in2434a:=integrate(acoth(z^(1/2))+log(abs(z-1)), z= 0..1,"noPole") --R --R --R log(16) + log(4) - 6log(2) ---R (218) -------------------------- +--R (185) -------------------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 220 +--E 185 ---S 221 of 267 +--S 186 of 224 in2443a:=integrate(sech(z)+log(abs(1-1/z^(1/3))), z= -1..1,"noPole") --R --R ---R (219) +--R (186) --R 3+---+2 3+---+ --R 3+---+2 3+---+ \|- 1 - 2\|- 1 + 1 --R log(\|- 1 - 2\|- 1 + 1) + log(---------------------) + 4atan(%e) @@ -5673,75 +5060,70 @@ in2443a:=integrate(sech(z)+log(abs(1-1/z^(1/3))), z= -1..1,"noPole") --R / --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 221 +--E 186 ---S 222 of 267 +--S 187 of 224 in2462a:=integrate(log((1+(1-z)^(1/2))/z)+csch(z), z= -1..0,"noPole") --R --R ---R (220) - infinity +--R (187) - infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 222 +--E 187 ---S 223 of 267 -in2469a:=integrate(1/(2+z)^2+1/(z^2-I*z-2)^(1/2), z= -1..1,"noPole") +--S 188 of 224 +in2469a:=integrate(1/(2+z)^2+1/(z^2-%i*z-2)^(1/2), z= -1..1,"noPole") --R --R ---R (221) ---R +-----+ 2 +-------+ 2 ---R 3log((4I + 8)\|I - 1 + I + 8I) - 3log((4I - 8)\|- I - 1 + I - 8I) + 4 ---R ------------------------------------------------------------------------- ---R 6 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 223 +--R (188) +--R +--------+ +--R 3log((8 + 4%i)\|- 1 + %i - 1 + 8%i) +--R + +--R +--------+ +--R - 3log((- 8 + 4%i)\|- 1 - %i - 1 - 8%i) + 4 +--R / +--R 6 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 188 ---S 224 of 267 +--S 189 of 224 in2484a:=integrate(log(1-z^2)+sinh(z^(1/2)), z= 0..%plusInfinity,"noPole") --R --R ---R (222) + infinity +--R (189) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 224 +--E 189 ---S 225 of 267 +--S 190 of 224 in2485a:=integrate(log(1-z^(1/2))-acoth(z^(1/2)), z= 0..1,"noPole") --R --R --R - log(16) + log(4) + 2log(2) - 10 ---R (223) --------------------------------- +--R (190) --------------------------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 225 +--E 190 ---S 226 of 267 +--S 191 of 224 in2521a:=integrate(acoth(z^(1/2))+cos(z^(1/2)-1), z= 0..1,"noPole") --R --R ---R (224) - 2cos(1) + 3 +--R (191) - 2cos(1) + 3 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 226 +--E 191 ---S 227 of 267 +--S 192 of 224 in2524a:=integrate(log(abs(1+1/z^(1/3)))+log(1+1/z), z= -1..0,"noPole") --R --R ---R (225) - infinity +--R (192) - infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 227 - ---S 228 of 267 -in2527a:=integrate(1/(1+I*z^(1/3))+cosh(z), z= %minusInfinity..0,"noPole") ---R ---R ---R (226) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 228 +--E 192 ---S 229 of 267 +--S 193 of 224 in2533a:=integrate(log(abs(1-1/z^(1/3)))-log(1-1/z), z= -1..0,"noPole") --R --R ---R (227) +--R (193) --R 3+---+2 3+---+ --R 3+---+2 3+---+ \|- 1 - 2\|- 1 + 1 3+---+2 --R - log(3\|- 1 + \|- 1 - 1) + log(---------------------) + \|- 1 @@ -5753,104 +5135,52 @@ in2533a:=integrate(log(abs(1-1/z^(1/3)))-log(1-1/z), z= -1..0,"noPole") --R / --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 229 +--E 193 ---S 230 of 267 +--S 194 of 224 in2566a:=integrate(log(1+(1-z)^(1/2))+acoth(1-z), z= -1..1,"noPole") --R --R --R +-+ +-+ --R 4log(\|2 + 1) + 4\|2 + 3log(9) - 4 ---R (228) ------------------------------------ +--R (194) ------------------------------------ --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 230 - ---S 231 of 267 -in2567a:=integrate(1/(I*z)^(1/3)*log(abs(z-1)), z= 0..1/2*%pi,"noPole") ---R ---R ---R (229) ---R 3+---+3+-----+2 3+-+3+---+2 3+-----+ 2 3+-+2 ---R 3+-+2 - I\|- I \|I %pi - 2I\|2 \|- I \|I %pi + I \|2 ---R 6I \|2 log(----------------------------------------------------) ---R 3+-+2 ---R \|2 ---R + ---R - ---R 3+-+2 ---R 3I \|2 ---R * ---R log ---R 3+---+3+-----+2 3+-+3+---+2 3+-----+ ---R - 6I\|- I \|I %pi + (I %pi + 4I)\|2 \|- I \|I %pi ---R + ---R 2 2 3+-+2 ---R (2I %pi + 2I )\|2 ---R / ---R 3+-+2 ---R 2\|2 ---R + ---R 3+---+2 3+-----+ 3+-+ ---R 3+-+2 +-+ 2\|- I \|I %pi + I\|2 ---R 12I \|2 \|3 atan(------------------------) ---R 3+-+ +-+ ---R I\|2 \|3 ---R + ---R 2 ---R %pi - 4%pi + 4 3+---+3+-----+2 3+-+2 2 ---R (6log(---------------) - 18)\|- I \|I %pi - 3I \|2 log(I ) ---R 4 ---R + ---R 3+-+2 +-+ ---R - 2I %pi \|2 \|3 ---R / ---R 3+-+2 3+---+ ---R 8I \|2 \|- I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 231 +--E 194 ---S 232 of 267 +--S 195 of 224 in2586a:=integrate(acoth(z^(1/2))+atan(z^(1/2)), z= 0..1,"noPole") --R --R --R log(16) - log(4) - 2log(2) + 2%pi ---R (230) --------------------------------- +--R (195) --------------------------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 232 +--E 195 ---S 233 of 267 +--S 196 of 224 in2591a:=integrate(log(z)/(1-z^(1/2))^3-log(z)*log(-z), z= 0..1,"noPole") --R --R ---R (231) - infinity +--R (196) - infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 233 - ---S 234 of 267 -in2597a:=integrate((1+I/z)^(1/2)-log(1-1/z^2), z= 0..%plusInfinity,"noPole") ---R ---R ---R (232) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 234 +--E 196 ---S 235 of 267 +--S 197 of 224 in2598a:=integrate(exp(-z^(1/2))+acoth(1-z^(1/2)), z= 0..1,"noPole") --R --R --R %e log(4) + %e - 4 ---R (233) ------------------ +--R (197) ------------------ --R %e --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 235 +--E 197 ---S 236 of 267 +--S 198 of 224 in2604a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..2,"noPole") --R --R ---R (234) +--R (198) --R 6+-+2 6+-+3 6+-+3 6+-+4 --R 18log(\|2 + 1) + 3log(- 2\|2 + 3) - 6log(- 4\|2 + 6) + 3\|2 --R + @@ -5859,55 +5189,54 @@ in2604a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..2,"noPole") --R / --R 6 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 236 +--E 198 ---S 237 of 267 +--S 199 of 224 in271a:=integrate(1/sqrt((z^2-1)*(z^2-1)), z= 2..%plusInfinity,"noPole") --R --R --R log(9) ---R (235) ------ +--R (199) ------ --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 237 +--E 199 ---S 238 of 267 -in275c:=integrate(sqrt(z), z= -I..I,"noPole") +--S 200 of 224 +in275c:=integrate(sqrt(z), z= -%i..%i,"noPole") --R --R ---R +-+ +---+ ---R 2I\|I + 2I\|- I ---R (236) ----------------- ---R 3 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 238 +--R +--+ +----+ +--R 2%i\|%i + 2%i\|- %i +--R (200) --------------------- +--R 3 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 200 ---S 239 of 267 -in275a:=integrate(1/(1+z), z= -I..I,"noPole") +--S 201 of 224 +in275a:=integrate(1/(1+z), z= -%i..%i,"noPole") --R --R ---R 2 2 ---R log(I + 2I + 1) - log(I - 2I + 1) ---R (237) ----------------------------------- ---R 2 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 239 +--R log(2%i) - log(- 2%i) +--R (201) --------------------- +--R 2 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 201 ---S 240 of 267 +--S 202 of 224 in275b:=integrate(1/(1+z), z= -%i..%i,"noPole") --R --R --R log(2%i) - log(- 2%i) ---R (238) --------------------- +--R (202) --------------------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) ---E 240 +--E 202 ---S 241 of 267 +--S 203 of 224 in276a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..sqrt(5)-2,"noPole") --R --R ---R (239) +--R (203) --R +-+ --R 3\|5 --R * @@ -5932,258 +5261,155 @@ in276a:=integrate(log(1-z^(1/3)-z^(2/3)), z= 0..sqrt(5)-2,"noPole") --R / --R 6 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 241 +--E 203 ---S 242 of 267 -in2634a:=integrate(1/(z^2+I*z-1)^(1/2)+log(abs(z-1)), z= -1..1,"noPole") +--S 204 of 224 +in2634a:=integrate(1/(z^2+%i*z-1)^(1/2)+log(abs(z-1)), z= -1..1,"noPole") --R --R ---R (240) ---R +---+ 2 +-+ 2 ---R log((- 4I + 8)\|- I + I - 8I + 4) - log((- 4I - 8)\|I + I + 8I + 4) +--R (204) +--R +----+ +--+ +--R log((8 - 4%i)\|- %i + 3 - 8%i) - log((- 8 - 4%i)\|%i + 3 + 8%i) --R + --R 2log(4) - 4 --R / --R 2 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 242 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 204 ---S 243 of 267 +--S 205 of 224 in2656a:=integrate(acoth(1-(1-z)^(1/2))-log(1-1/z), z= -1..1,"noPole") --R --R ---R (241) +--R (205) --R +-+ +-+ +-+ +-+ --R - 10log(\|2 ) + log(- 2\|2 + 3) - 3log(- 4\|2 + 6) - 4\|2 + 2log(4) --R ---------------------------------------------------------------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 243 +--E 205 ---S 244 of 267 +--S 206 of 224 in2676a:=integrate(acoth(1-(1-z)^(1/2))-log(1-1/z), z= -1..1,"noPole") --R --R ---R (242) +--R (206) --R +-+ +-+ +-+ +-+ --R - 10log(\|2 ) + log(- 2\|2 + 3) - 3log(- 4\|2 + 6) - 4\|2 + 2log(4) --R ---------------------------------------------------------------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 244 +--E 206 ---S 245 of 267 +--S 207 of 224 in2664aa:=integrate(atanh(1/z)+(1+z^2)^(1/2), z= 0..%plusInfinity,"noPole") --R --R ---R (243) + infinity +--R (207) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 245 +--E 207 ---S 246 of 267 -in2681a:=integrate((z^2-I*z-3)^(1/2)+%pi-acot(z-1), z= -1..1,"noPole") +--S 208 of 224 +in2681a:=integrate((z^2-%i*z-3)^(1/2)+%pi-acot(z-1), z= -1..1,"noPole") --R --R ---R (244) ---R 4 2 +-------+ 5 4 3 2 ---R (- 16I - 128I + 768)\|- I - 2 - 4I + 24I + 32I + 320I ---R + ---R 960I + 384 ---R * ---R +-----+ ---R \|I - 2 ---R + ---R 5 4 3 2 +-------+ 6 4 ---R (- 4I - 24I + 32I - 320I + 960I - 384)\|- I - 2 - I + 60I +--R (208) +--R +--------+ +--------+ +--------+ +--R (- 880\|- 2 - %i - 88 - 924%i)\|- 2 + %i + (88 - 924%i)\|- 2 - %i --R + ---R 2 ---R 848I - 192 +--R 979 --R * ---R +-----+ 2 ---R log((4I + 8)\|I - 2 + I + 8I - 4) +--R +--------+ +--R log((8 + 4%i)\|- 2 + %i - 5 + 8%i) --R + ---R 4 2 +-------+ 5 4 3 2 ---R (16I + 128I - 768)\|- I - 2 + 4I - 24I - 32I - 320I - 960I ---R + ---R - 384 ---R * ---R +-----+ ---R \|I - 2 +--R +--------+ +--------+ +--------+ +--R (880\|- 2 - %i + 88 + 924%i)\|- 2 + %i + (- 88 + 924%i)\|- 2 - %i --R + ---R 5 4 3 2 +-------+ 6 4 ---R (4I + 24I - 32I + 320I - 960I + 384)\|- I - 2 + I - 60I ---R + ---R 2 ---R - 848I + 192 +--R - 979 --R * ---R +-------+ 2 ---R log((4I - 8)\|- I - 2 + I - 8I - 4) +--R +--------+ +--R log((- 8 + 4%i)\|- 2 - %i - 5 - 8%i) --R + ---R 2 2 4 2 ---R (64I - 256)log(25) + (256I - 1024)atan(-) + (512I - 2048)%pi ---R 3 ---R + ---R 3 ---R 256I - 1024I ---R * ---R +-------+ ---R \|- I - 2 ---R + ---R 3 2 ---R (16I - 96I - 320I - 128)log(25) +--R - 4 + 3%i +--------+ +--R (320log(25) - 640%i log(---------) + 2560%pi + 1280%i)\|- 2 - %i +--R 4 + 3%i --R + ---R 3 2 4 ---R (64I - 384I - 1280I - 512)atan(-) ---R 3 +--R - 4 + 3%i +--R (32 + 336%i)log(25) + (672 - 64%i)log(---------) + (256 + 2688%i)%pi +--R 4 + 3%i --R + ---R 3 2 5 4 3 2 ---R (128I - 768I - 2560I - 1024)%pi + 4I + 72I - 288I - 1088I + 64I ---R + ---R 1152 +--R - 2312 - 356%i --R * ---R +-----+ ---R \|I - 2 +--R +--------+ +--R \|- 2 + %i --R + ---R 3 2 ---R (16I + 96I - 320I + 128)log(25) ---R + ---R 3 2 4 ---R (64I + 384I - 1280I + 512)atan(-) ---R 3 ---R + ---R 3 2 5 4 3 2 ---R (128I + 768I - 2560I + 1024)%pi - 4I + 72I + 288I - 1088I - 64I +--R - 4 + 3%i +--R (- 32 + 336%i)log(25) + (672 + 64%i)log(---------) +--R 4 + 3%i --R + ---R 1152 +--R (- 256 + 2688%i)%pi - 2312 + 356%i --R * ---R +-------+ ---R \|- I - 2 +--R +--------+ +--R \|- 2 - %i --R + ---R 4 2 4 2 4 ---R (4I - 288I + 64)log(25) + (16I - 1152I + 256)atan(-) ---R 3 ---R + ---R 4 2 5 3 ---R (32I - 2304I + 512)%pi + 32I - 768I + 2560I +--R - 4 + 3%i +--R - 356log(25) + 712%i log(---------) - 2848%pi - 3360%i +--R 4 + 3%i --R / ---R 2 +-------+ 3 2 +-----+ ---R ((256I - 1024)\|- I - 2 + 64I - 384I - 1280I - 512)\|I - 2 ---R + ---R 3 2 +-------+ 4 2 ---R (64I + 384I - 1280I + 512)\|- I - 2 + 16I - 1152I + 256 ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 246 - ---S 247 of 267 -in2691a:=integrate(1/(z^2+I*z-1)^(1/2)+(1-I*z)^(1/2), z= -1..1,"noPole") ---R ---R ---R (245) ---R +---+ 2 ---R 3I log((- 4I + 8)\|- I + I - 8I + 4) ---R + ---R +-+ 2 +-----+ ---R - 3I log((- 4I - 8)\|I + I + 8I + 4) + (4I + 4)\|I + 1 +--R +--------+ +--------+ +--------+ +--R (1280\|- 2 - %i + 128 + 1344%i)\|- 2 + %i + (- 128 + 1344%i)\|- 2 - %i --R + ---R +-------+ ---R (4I - 4)\|- I + 1 ---R / ---R 6I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 247 +--R - 1424 +--R Type: Union(f1: OrderedCompletion Expression Complex Integer,...) +--E 208 +--S 209 of 224 in2720a:=integrate(acoth(1-(1-z)^(1/2))+atan(z-1), z= 0..1,"noPole") --R --R --R 5log(4) - %pi - 4 ---R (246) ----------------- +--R (209) ----------------- --R 4 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 248 +--E 209 ---S 249 of 267 +--S 210 of 224 in2724a:=integrate(log(1-1/z^3)-(1+1/z^2)^(1/2), z= 0..%plusInfinity,"noPole") --R --R ---R (247) - infinity +--R (210) - infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 249 +--E 210 ---S 250 of 267 +--S 211 of 224 in2732:=integrate(atan(1/3*3^(1/2)*(2*z-1)), z= 0..%plusInfinity) --R --R ---R (248) - infinity +--R (211) - infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 250 +--E 211 ---S 251 of 267 +--S 212 of 224 in2783a:=integrate(1/z^(1/3)+atanh(1/z^(1/2)), z= 0..%plusInfinity,"noPole") --R --R ---R (249) + infinity +--R (212) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 251 - ---S 252 of 267 -in2815a:=integrate((I*z)^(1/2)-(1+1/(I*z)^(1/2))^(1/2), z= -1..1,"noPole") ---R ---R ---R (250) ---R +----------+ +--------+ ---R | +---+ | +-+ ---R |\|- I + 1 |\|I + 1 ---R - 6log( |---------- + 1) + 6log( |-------- + 1) ---R | +---+ | +-+ ---R \| \|- I \| \|I ---R + ---R +--------+ ---R | +-+ ---R +-+ |\|I + 1 +-+ ---R - 2\|I |-------- + 2\|I + 1 ---R | +-+ ---R \| \|I ---R - 3log(------------------------------) ---R +-+ ---R \|I ---R + ---R +----------+ ---R | +---+ ---R +---+ |\|- I + 1 +---+ ---R - 2\|- I |---------- + 2\|- I + 1 ---R | +---+ ---R \| \|- I ---R 3log(------------------------------------) ---R +---+ ---R \|- I ---R + ---R +----------+ +--------+ ---R | +---+ | +-+ ---R +---+ |\|- I + 1 +-+ |\|I + 1 +-+ ---R (12\|- I - 24I) |---------- + (- 12\|I - 24I) |-------- + 16I\|I ---R | +---+ | +-+ ---R \| \|- I \| \|I ---R + ---R +---+ ---R 16I\|- I ---R / ---R 24I ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 252 +--E 212 ---S 253 of 267 +--S 213 of 224 in285:=integrate(sqrt(1+sqrt(z-1)), z) --R --R --R +------------+ --R +-----+ | +-----+ --R (4\|z - 1 + 12z - 20)\|\|z - 1 + 1 ---R (251) ------------------------------------- +--R (213) ------------------------------------- --R 15 --R Type: Union(Expression Integer,...) ---E 253 +--E 213 ---S 254 of 267 +--S 214 of 224 in295a:=integrate(z*sqrt(1+sqrt(z^2-1)), z) --R --R @@ -6191,285 +5417,71 @@ in295a:=integrate(z*sqrt(1+sqrt(z^2-1)), z) --R +------+ | +------+ --R | 2 2 | | 2 --R (2\|z - 1 + 6z - 10)\|\|z - 1 + 1 ---R (252) --------------------------------------- +--R (214) --------------------------------------- --R 15 --R Type: Union(Expression Integer,...) ---E 254 +--E 214 ---S 255 of 267 +--S 215 of 224 in295ba:=integrate(z*sqrt(1+sqrt(z^2-1)), z= 1..sqrt(2),"noPole") --R --R --R +-+ --R 4\|2 + 4 ---R (253) --------- +--R (215) --------- --R 15 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 255 +--E 215 ---S 256 of 267 +--S 216 of 224 integrate(1/sqrt(20+x^2+y^2), x = -5..5,"noPole") --R --R --R +-------+ +-------+ --R | 2 2 | 2 2 --R log(10\|y + 45 + y + 70) - log(- 10\|y + 45 + y + 70) ---R (254) ----------------------------------------------------------- +--R (216) ----------------------------------------------------------- --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 256 +--E 216 ---S 257 of 267 +--S 217 of 224 in291:=integrate(cos(2*atan(z-sqrt(2)))-sin(2*atan(z-sqrt(2))), z = 0..%plusInfinity) --R --R ---R (255) - infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 257 - ---S 258 of 267 -in2924a:=integrate(1/(I*z)^(1/2)+(1+1/(I*z)^(1/2))^(1/2), z= -1..1,"noPole") ---R ---R ---R (256) ---R +----------+ +--------+ ---R | +---+ | +-+ ---R +---+ +-+ |\|- I + 1 +---+ +-+ |\|I + 1 ---R 2\|- I \|I log( |---------- + 1) - 2\|- I \|I log( |-------- + 1) ---R | +---+ | +-+ ---R \| \|- I \| \|I ---R + ---R +--------+ ---R | +-+ ---R +-+ |\|I + 1 +-+ ---R - 2\|I |-------- + 2\|I + 1 ---R | +-+ ---R +---+ +-+ \| \|I ---R \|- I \|I log(------------------------------) ---R +-+ ---R \|I ---R + ---R +----------+ ---R | +---+ ---R +---+ |\|- I + 1 +---+ ---R - 2\|- I |---------- + 2\|- I + 1 ---R | +---+ ---R +---+ +-+ \| \|- I ---R - \|- I \|I log(------------------------------------) ---R +---+ ---R \|- I ---R + ---R +----------+ +--------+ ---R | +---+ | +-+ ---R +---+ +-+ |\|- I + 1 +---+ +-+ +---+ |\|I + 1 ---R (8I\|- I + 4I)\|I |---------- + (8I\|- I \|I + 4I\|- I ) |-------- ---R | +---+ | +-+ ---R \| \|- I \| \|I ---R + ---R +-+ +---+ ---R 16I\|I + 16I\|- I ---R / ---R +---+ +-+ ---R 8I\|- I \|I +--R (217) - infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 258 - ---S 259 of 267 -in2963a:=integrate(cosh(-1+(1-z)^(1/2))+(z^2+I*z-3)^(1/2), z= -1..1,"noPole") ---R ---R ---R (257) ---R +-+ ---R 4 2 \|2 - 1 +-------+ ---R (- 16I - 128I + 768)%e %e \|- I - 2 ---R + ---R +-+ ---R 5 4 3 2 \|2 - 1 ---R (4I - 24I - 32I - 320I - 960I - 384)%e %e ---R * ---R +-----+ ---R \|I - 2 ---R + ---R +-+ ---R 5 4 3 2 \|2 - 1 +-------+ ---R (4I + 24I - 32I + 320I - 960I + 384)%e %e \|- I - 2 ---R + ---R +-+ ---R 6 4 2 \|2 - 1 ---R (- I + 60I + 848I - 192)%e %e ---R * ---R +-------+ 2 ---R log((- 4I + 8)\|- I - 2 + I - 8I - 4) ---R + ---R +-+ ---R 4 2 \|2 - 1 +-------+ ---R (16I + 128I - 768)%e %e \|- I - 2 ---R + ---R +-+ ---R 5 4 3 2 \|2 - 1 ---R (- 4I + 24I + 32I + 320I + 960I + 384)%e %e ---R * ---R +-----+ ---R \|I - 2 ---R + ---R +-+ ---R 5 4 3 2 \|2 - 1 +-------+ ---R (- 4I - 24I + 32I - 320I + 960I - 384)%e %e \|- I - 2 ---R + ---R +-+ ---R 6 4 2 \|2 - 1 ---R (I - 60I - 848I + 192)%e %e ---R * ---R +-----+ 2 ---R log((- 4I - 8)\|I - 2 + I + 8I - 4) ---R + ---R +-+ 2 ---R 2 +-+ 2 \|2 - 1 ---R ((256I - 1024)%e\|2 + (- 256I + 1024)%e)(%e ) ---R + ---R 2 2 3 2 ---R ((256I - 1024)%e + (- 256I + 1024I)%e + 256I - 1024) ---R * ---R +-+ ---R \|2 - 1 ---R %e ---R + ---R 2 +-+ 2 ---R (- 256I + 1024)%e\|2 + (- 256I + 1024)%e ---R * ---R +-------+ ---R \|- I - 2 ---R + ---R 3 2 +-+ ---R (- 64I + 384I + 1280I + 512)%e\|2 ---R + ---R 3 2 ---R (64I - 384I - 1280I - 512)%e ---R * ---R +-+ 2 ---R \|2 - 1 ---R (%e ) ---R + ---R 3 2 2 ---R (- 64I + 384I + 1280I + 512)%e ---R + ---R 5 4 3 2 3 2 ---R (4I + 72I - 288I - 1088I + 64I + 1152)%e - 64I + 384I ---R + ---R 1280I + 512 ---R * ---R +-+ ---R \|2 - 1 ---R %e ---R + ---R 3 2 +-+ 3 2 ---R (64I - 384I - 1280I - 512)%e\|2 + (64I - 384I - 1280I - 512)%e ---R * ---R +-----+ ---R \|I - 2 ---R + ---R 3 2 +-+ ---R (- 64I - 384I + 1280I - 512)%e\|2 ---R + ---R 3 2 ---R (64I + 384I - 1280I + 512)%e ---R * ---R +-+ 2 ---R \|2 - 1 ---R (%e ) ---R + ---R 3 2 2 ---R (- 64I - 384I + 1280I - 512)%e ---R + ---R 5 4 3 2 3 2 ---R (- 4I + 72I + 288I - 1088I - 64I + 1152)%e - 64I - 384I ---R + ---R 1280I - 512 ---R * ---R +-+ ---R \|2 - 1 ---R %e ---R + ---R 3 2 +-+ 3 2 ---R (64I + 384I - 1280I + 512)%e\|2 + (64I + 384I - 1280I + 512)%e ---R * ---R +-------+ ---R \|- I - 2 ---R + ---R +-+ 2 ---R 4 2 +-+ 4 2 \|2 - 1 ---R ((16I - 1152I + 256)%e\|2 + (- 16I + 1152I - 256)%e)(%e ) ---R + ---R 4 2 2 5 3 4 2 ---R (16I - 1152I + 256)%e + (- 32I + 768I - 2560I)%e + 16I - 1152I ---R + ---R 256 ---R * ---R +-+ ---R \|2 - 1 ---R %e ---R + ---R 4 2 +-+ 4 2 ---R (- 16I + 1152I - 256)%e\|2 + (- 16I + 1152I - 256)%e ---R / ---R +-+ ---R 2 \|2 - 1 +-------+ ---R (256I - 1024)%e %e \|- I - 2 ---R + ---R +-+ ---R 3 2 \|2 - 1 ---R (- 64I + 384I + 1280I + 512)%e %e ---R * ---R +-----+ ---R \|I - 2 ---R + ---R +-+ ---R 3 2 \|2 - 1 +-------+ ---R (- 64I - 384I + 1280I - 512)%e %e \|- I - 2 ---R + ---R +-+ ---R 4 2 \|2 - 1 ---R (16I - 1152I + 256)%e %e ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 259 +--E 217 ---S 260 of 267 +--S 218 of 224 in2992a:=integrate(acoth(1-z^(1/2))+log(1+z^(1/3)), z= 1..%plusInfinity,"noPole") --R --R ---R (258) + infinity +--R (218) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 260 +--E 218 ---S 261 of 267 +--S 219 of 224 in2997a:=integrate(log(1+1/z^3)-log(abs(1+z)), z= %minusInfinity..%plusInfinity,"noPole") --R --R ---R (259) - infinity +--R (219) - infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 261 - ---S 262 of 267 -in3001a:=integrate(((I*z)^(1/2)-1)/(-2+(I*z)^(1/2)), z= 0..%plusInfinity,"noPole") ---R ---R ---R (260) + infinity ---R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 262 +--E 219 ---S 263 of 267 +--S 220 of 224 in3008a:=integrate(exp(-z^(1/3))+atanh(1/z^(1/2)), z= 0..%plusInfinity,"noPole") --R --R ---R (261) + infinity +--R (220) + infinity --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 263 +--E 220 ---S 264 of 267 +--S 221 of 224 in303a:=integrate(1/(1+cosh(n*z)^2), z= 0..1,"noPole") --R --R ---R (262) +--R (221) --R log --R +-+ - n 8 +-+ - n 6 --R (- 816\|2 + 1154)(%e ) + (- 560\|2 + 792)(%e ) @@ -6486,13 +5498,13 @@ in303a:=integrate(1/(1+cosh(n*z)^2), z= 0..1,"noPole") --R +-+ --R 4n\|2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 264 +--E 221 ---S 265 of 267 +--S 222 of 224 in314a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole") --R --R ---R (263) +--R (222) --R log --R 2 2 --R - 12sin(1) + (42cos(1) + 48)sin(1) - 36cos(1) - 84cos(1) @@ -6514,25 +5526,25 @@ in314a:=integrate(1/(sin(z)-1/2), z= 0..1,"noPole") --R +-+ --R \|3 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 265 +--E 222 ---S 266 of 267 +--S 223 of 224 in317:=integrate((cos(z)^a)^(1/a), z= 0..%pi) --R --R ---R (264) 0 +--R (223) 0 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 266 +--E 223 ---S 267 of 267 +--S 224 of 224 in319a:=integrate(exp(-z)*atan(sin(z)/(1+cos(z))), z=0..%plusInfinity,"noPole") --R --R --R 1 ---R (265) - +--R (224) - --R 2 --R Type: Union(f1: OrderedCompletion Expression Integer,...) ---E 267 +--E 224 )spool )lisp (bye)