727 lines
14 KiB
C++
727 lines
14 KiB
C++
// For testing the integral function
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#include "stdafx.h"
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#include "defs.h"
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#if SELFTEST
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static char *s[] = {
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"clear",
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"",
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"tty=1",
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"",
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"integral(x^2+x)-(1/2*x^2+1/3*x^3)",
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"0",
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"#1",
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"integral(A,X)",
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"A*X",
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"#4",
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"integral(A+B,X)-(A*X+B*X)",
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"0",
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"#9",
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"integral(1/X,X)",
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"log(X)",
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"#11",
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"integral(exp(X),X)",
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"exp(X)",
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"#12",
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"integral(exp(A*X),X)-exp(A*X)/A",
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"0",
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"#14",
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"integral(log(X),X)-X*log(X)+X",
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"0",
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"#15",
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"integral(3^X*log(3),X)",
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"3^X",
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"#16",
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"integral(1/(3+x^2),x)-3^(-1/2)*arctan(3^(-1/2)*x)",
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"0",
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"#17",
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"integral(1/(a-x^2),x)-a^(-1/2)*arctanh(a^(-1/2)*x)",
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"0",
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"#19",
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"integral(1/sqrt(a-x^2),x)-arcsin(a^(-1/2)*x)",
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"0",
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"#20",
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"integral(1/sqrt(a+x^2),x)-(log(x+(a+x^2)^(1/2)))",
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"0",
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"#27",
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"integral(1/(a+b*x),x)-(log(a+b*x)/b)",
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"0",
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"#28",
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"integral(1/(A+B*X)^2,X)+1/B*1/(A+B*X)",
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"0",
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"#29",
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"integral(1/(a+b*x)^3,x)+1/2*1/b*(a+b*x)^(-2)",
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"0",
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"#30",
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"integral(X/(A+B*X),X)+A*B^(-2)*log(A+B*X)-X/B",
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"0",
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"#31",
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"integral(X/(A+B*X)^2,X)-1/B^2*(log(A+B*X)+A/(A+B*X))",
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"0",
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"#33",
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"integral(X^2/(A+B*X),X)-1/B^2*(1/2*(A+B*X)^2-2*A*(A+B*X)+A^2*log(A+B*X))",
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"0",
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"#34",
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"integral(X^2/(A+B*X)^2,X)-1/B^3*(A+B*X-2*A*log(A+B*X)-A^2/(A+B*X))",
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"0",
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"#35",
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"integral(X^2/(A+B*X)^3,X)-1/B^3*(log(A+B*X)+2*A/(A+B*X)-1/2*A^2/(A+B*X)^2)",
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"0",
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"#37",
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"integral(1/X*1/(A+B*X),X)+1/A*log((A+B*X)/X)",
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"0",
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"#38",
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"integral(1/X*1/(A+B*X)^2,X)-1/A*1/(A+B*X)+1/A^2*log((A+B*X)/X)",
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"0",
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"#39",
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"integral(1/X*1/(A+B*X)^3,X)-1/A^3*(1/2*((2*A+B*X)/(A+B*X))^2+log(X/(A+B*X)))",
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"0",
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"#40",
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"integral(1/X^2*1/(A+B*X),X)+1/(A*X)-B/A^2*log((A+B*X)/X)",
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"0",
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"#41",
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"integral(1/X^3*1/(A+B*X),X)-(2*B*X-A)/(2*A^2*X^2)-B^2/A^3*log(X/(A+B*X))",
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"0",
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"#42",
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"integral(1/X^2*1/(A+B*X)^2,X)+(A+2*B*X)/(A^2*X*(A+B*X))-2*B/A^3*log((A+B*X)/X)",
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"0",
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"#60",
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"integral(1/(2+3*X^2),X)-1/sqrt(6)*arctan(1/2*X*sqrt(6))",
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"0",
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"integral(1/(-2-3*X^2),X)-1/sqrt(6)*arctan(-1/2*X*sqrt(6))",
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"0",
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"#61",
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"integral(1/(2-3*X^2),X)-1/2*1/sqrt(6)*log((2+X*sqrt(6))/(2-X*sqrt(6)))",
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"0",
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"integral(1/(-2+3*X^2),X)-1/2*1/sqrt(6)*log((-2+X*sqrt(6))/(-2-X*sqrt(6)))",
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"0",
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"#63",
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"integral(X/(A+B*X^2),X)-1/2*1/B*log(A+B*X^2)",
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"0",
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"#64",
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"integral(X^2/(A+B*X^2),X)-X/B+A/B*integral(1/(A+B*X^2),X)",
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"0",
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"#65",
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"integral(1/(A+B*X^2)^2,X)-X/(2*A*(A+B*X^2))-1/2*1/A*integral(1/(A+B*X^2),X)",
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"0",
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"#70",
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"integral(1/X*1/(A+B*X^2),X)-1/2*1/A*log(X^2/(A+B*X^2))",
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"0",
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"#71",
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"integral(1/X^2*1/(A+B*X^2),X)+1/(A*X)+B/A*integral(1/(A+B*X^2),X)",
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"0",
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"#74",
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"integral(1/(A+B*X^3),X)-1/3*1/A*(A/B)^(1/3)*(1/2*log(((A/B)^(1/3)+X)^3/(A+B*X^3))+sqrt(3)*arctan((2*X-(A/B)^(1/3))*(A/B)^(-1/3)/sqrt(3)))",
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"0",
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"#76",
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"integral(X^2/(A+B*X^3),X)-1/3*1/B*log(A+B*X^3)",
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"0",
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"#77",
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"integral(1/(2+3*X^4),X)-1/2*1/2*(2/3/4)^(1/4)*(1/2*log((X^2+2*(2/3/4)^(1/4)*X+2*(2/3/4)^(1/2))/(X^2-2*(2/3/4)^(1/4)*X+2*(2/3/4)^(1/2)))+arctan(2*(2/3/4)^(1/4)*X/(2*(2/3/4)^(1/2)-X^2)))",
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"0",
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"#78",
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"integral(1/(2-3*X^4),X)-1/2*(2/3)^(1/4)/2*(1/2*log((X+(2/3)^(1/4))/(X-(2/3)^(1/4)))+arctan(X*(2/3)^(-1/4)))",
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"0",
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"#79",
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"integral(X/(2+3*X^4),X)-1/2*1/3*1/sqrt(2/3)*arctan(X^2/sqrt(2/3))",
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"0",
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"#80",
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"integral(X/(2-3*X^4),X)+1/4*1/3*sqrt(3/2)*log((X^2-sqrt(2/3))/(X^2+sqrt(2/3)))",
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"0",
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"#81",
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"integral(X^2/(2+3*X^4),X)-1/4*1/3*(2/3/4)^(-1/4)*(1/2*log((X^2-2*(2/3/4)^(1/4)*X+2*sqrt(2/3/4))/(X^2+2*(2/3/4)^(1/4)*X+2*sqrt(2/3/4)))+arctan(2*(2/3/4)^(1/4)*X/(2*sqrt(2/3/4)-X^2)))",
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"0",
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"#82",
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"integral(X^2/(2-3*X^4),X)+1/4*1/3*(2/3)^(-1/4)*(log((X-(2/3)^(1/4))/(X+(2/3)^(1/4)))+2*arctan(X*(2/3)^(-1/4)))",
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"0",
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"#83",
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"integral(X^3/(A+B*X^4),X)-1/4*1/B*log(A+B*X^4)",
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"0",
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"#124",
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"integral(sqrt(A+B*X),X)-2/3/B*sqrt((A+B*X)^3)",
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"0",
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"#125",
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"integral(X*sqrt(A+B*X),X)+2*(2*A-3*B*X)*sqrt((A+B*X)^3)/15*B^(-2)",
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"0",
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"#126",
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"integral(X^2*sqrt(A+B*X),X)-2*(8*A^2-12*A*B*X+15*B^2*X^2)*sqrt((A+B*X)^3)/105*B^(-3)",
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"0",
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"#128",
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"integral(sqrt(A+B*X)/X,X)-2*sqrt(A+B*X)-A*integral(1/X*1/sqrt(A+B*X),X)",
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"0",
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"#129",
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"integral(sqrt(A+B*X)/X^2,X)+sqrt(A+B*X)/X-B/2*integral(1/X*1/sqrt(A+B*X),X)",
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"0",
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"#131",
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"integral(1/sqrt(A+B*X),X)-2*sqrt(A+B*X)/B",
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"0",
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"#132",
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"integral(X/sqrt(A+B*X),X)+2/3*(2*A-B*X)*sqrt(A+B*X)/B^2",
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"0",
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"#133",
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"integral(X^2/sqrt(A+B*X),X)-2/15*(8*A^2-4*A*B*X+3*B^2*X^2)*sqrt(A+B*X)/B^3",
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"0",
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"#134",
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"integral(1/X*1/sqrt(2+B*X),X)-1/sqrt(2)*log((sqrt(2+B*X)-sqrt(2))/(sqrt(2+B*X)+sqrt(2)))",
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"0",
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"#136",
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"integral(1/X*1/sqrt(-2+B*X),X)-2/sqrt(2)*arctan(sqrt((-2+B*X)/2))",
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"0",
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"#137",
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"integral(1/X^2*1/sqrt(A+B*X),X)+sqrt(A+B*X)/A/X+1/2*B/A*integral(1/X*1/sqrt(A+B*X),X)",
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"0",
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"#156",
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"integral(sqrt(X^2+A),X)-1/2*(X*sqrt(X^2+A)+A*log(X+sqrt(X^2+A)))",
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"0",
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"#157",
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"integral(1/sqrt(X^2+A),X)-log(X+sqrt(X^2+A))",
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"0",
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"#158",
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"integral(1/X*1/sqrt(X^2-2),X)-arcsec(X/sqrt(2))/sqrt(2)",
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"0",
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"#159",
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"integral(1/X*1/sqrt(X^2+2),X)+1/sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X)",
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"0",
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"#160",
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"integral(sqrt(X^2+2)/X,X)-sqrt(X^2+2)+sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X)",
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"0",
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"#161",
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"integral(sqrt(X^2-2)/X,X)-sqrt(X^2-2)+sqrt(2)*arcsec(X/sqrt(2))",
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"0",
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"#162",
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"integral(X/sqrt(X^2+A),X)-sqrt(X^2+A)",
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"0",
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"#163",
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"integral(X*sqrt(X^2+A),X)-1/3*sqrt((X^2+A)^3)",
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"0",
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"#164",
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"integral(sqrt((X^2+A)^3),X)-1/4*(X*sqrt((X^2+A)^3)+3/2*A*X*sqrt(X^2+A)+3/2*A^2*log(X+sqrt(X^2+A)))",
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"0",
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// "integral(sqrt((X^2-A)^3),X)-1/4*(X*sqrt((X^2-A)^3)-3/2*A*X*sqrt(X^2-A)+3/2*A^2*log(X+sqrt(X^2-A)))",
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// "0",
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"#165",
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"integral(1/sqrt((X^2+A)^3),X)-X/A/sqrt(X^2+A)",
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"0",
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"#166",
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"integral(X/sqrt((X^2+A)^3),X)+1/sqrt(X^2+A)",
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"0",
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"#167",
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"integral(X*sqrt((X^2+A)^3),X)-1/5*sqrt((X^2+A)^5)",
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"0",
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"#168",
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"integral(X^2*sqrt(X^2+A),X)-1/4*X*sqrt((X^2+A)^3)+1/8*A*X*sqrt(X^2+A)+1/8*A^2*log(X+sqrt(X^2+A))",
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"0",
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"#169",
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"integral(X^3*sqrt(X^2+7),X)-(1/5*X^2-2/15*7)*sqrt((X^2+7)^3)",
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"0",
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"#170",
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"integral(X^3*sqrt(X^2-7),X)-(sqrt((X^2-7)^5)/5+7*sqrt((X^2-7)^3)/3)",
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"0",
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"#171",
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"integral(X^2/sqrt(X^2+A),X)-1/2*X*sqrt(X^2+A)+1/2*A*log(X+sqrt(X^2+A))",
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"0",
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"#172",
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"integral(X^3/sqrt(X^2+A),X)-1/3*sqrt((X^2+A)^3)+A*sqrt(X^2+A)",
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"0",
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"#173",
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"integral(1/X^2*1/sqrt(X^2+A),X)+sqrt(X^2+A)/A/X",
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"0",
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"#174",
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"integral(1/X^3*1/sqrt(X^2+2),X)+1/2*sqrt(X^2+2)/2/X^2-1/2*log((sqrt(2)+sqrt(X^2+2))/X)/(sqrt(2)^3)",
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"0",
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"#175",
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"integral(1/X^3*1/sqrt(X^2-2),X)-1/2*sqrt(X^2-2)/2/X^2-1/2*1/(2^(3/2))*arcsec(X/(2^(1/2)))",
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"0",
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"#176+",
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"integral(X^2*sqrt((X^2+2^2)^3),X)"
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"-1/6*X*sqrt((X^2+2^2)^5)"
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"+1/24*(2^2)*X*sqrt((X^2+2^2)^3)"
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"+1/16*(2^4)X*sqrt(X^2+2^2)"
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"+1/16*(2^6)*log(X+sqrt(X^2+2^2))",
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"0",
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"#176-",
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"integral(X^2*sqrt((X^2-2^2)^3),X)"
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"-1/6*X*sqrt((X^2-2^2)^5)"
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"-1/24*(2^2)*X*sqrt((X^2-2^2)^3)"
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"+1/16*(2^4)X*sqrt(X^2-2^2)"
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"-1/16*(2^6)*log(X+sqrt(X^2-2^2))",
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"0",
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"#177+",
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"integral(X^3*sqrt((X^2+7^2)^3),X)"
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"-1/7*sqrt((X^2+7^2)^7)"
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"+1/5*(7^2)*sqrt((X^2+7^2)^5)",
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"0",
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"#177-",
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"integral(X^3*sqrt((X^2-7^2)^3),X)"
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"-1/7*sqrt((X^2-7^2)^7)"
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"-1/5*(7^2)*sqrt((X^2-7^2)^5)",
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"0",
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"#196",
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"simplify(integral(1/(X-A)/sqrt(X^2-A^2),X)+sqrt(X^2-A^2)/A/(X-A))",
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"0",
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"simplify(1/(X-A)/sqrt(X^2-A^2)-d(integral(1/(X-A)/sqrt(X^2-A^2),X),X))",
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"0",
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"#197",
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"integral(1/(X+A)/sqrt(X^2-A^2),X)-sqrt(X^2-A^2)/A/(X+A)",
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"0",
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"simplify(1/(X+A)/sqrt(X^2-A^2)-d(integral(1/(X+A)/sqrt(X^2-A^2),X),X))",
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"0",
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"#200",
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"integral(sqrt(7-X^2),X)-1/2*(X*sqrt(7-X^2)+7*arcsin(X/sqrt(7)))",
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"0",
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"#201",
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"integral(1/sqrt(7-X^2),X)-arcsin(X/sqrt(7))",
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"0",
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"#202",
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"integral(1/X*1/sqrt(7-X^2),X)+1/sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X)",
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"0",
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"#203",
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"integral(sqrt(7-X^2)/X,X)"
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"-sqrt(7-X^2)+sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X)",
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"0",
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"#204",
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"integral(X/sqrt(A-X^2),X)"
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"+sqrt(A-X^2)",
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"0",
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"#205",
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"integral(X*sqrt(A-X^2),X)"
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"+1/3*sqrt((A-X^2)^3)",
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"0",
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"#210",
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"integral(X^2*sqrt(7-X^2),X)"
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"+1/4*X*sqrt((7-X^2)^3)"
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"-7/8*(X*sqrt(7-X^2)+7*arcsin(X/sqrt(7)))",
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"0",
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"#211",
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"integral(X^3*sqrt(7-X^2),X)"
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"-(-1/5*X^2-2/15*7)*sqrt((7-X^2)^3)",
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"0",
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"#214",
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"integral(X^2/sqrt(7-X^2),X)"
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"+X/2*sqrt(7-X^2)"
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"-7/2*arcsin(X/sqrt(7))",
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"0",
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"#215",
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"integral(1/X^2*1/sqrt(7-X^2),X)"
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"+sqrt(7-X^2)/7/X",
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"0",
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"#216",
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"integral(sqrt(7-X^2)/X^2,X)"
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"+sqrt(7-X^2)/X"
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"+arcsin(X/sqrt(7))",
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"0",
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"#217",
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"integral(sqrt(7-X^2)/X^3,X)"
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"+1/2*sqrt(7-X^2)/X^2"
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"-1/2*log((sqrt(7)+sqrt(7-X^2))/X)/sqrt(7)",
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"0",
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"#218",
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"integral(sqrt(7-X^2)/X^4,X)"
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|
"+1/3*sqrt((7-X^2)^3)/7/X^3",
|
|
"0",
|
|
|
|
"#273",
|
|
"integral(sqrt(7*X^2+C),X)-X*sqrt(7*X^2+C)/2-C*log(X*sqrt(7)+sqrt(7*X^2+C))/2/sqrt(7)",
|
|
"0",
|
|
|
|
"#274",
|
|
"integral(sqrt(-7*X^2+C),X)-X*sqrt(-7*X^2+C)/2-C*arcsin(X*sqrt(7/C))/2/sqrt(7)",
|
|
"0",
|
|
|
|
"#290",
|
|
"integral(sin(A*X),X)+cos(A*X)/A",
|
|
"0",
|
|
|
|
"#291",
|
|
"integral(cos(A*X),X)-sin(A*X)/A",
|
|
"0",
|
|
|
|
"#292",
|
|
"integral(tan(A*X),X)+log(cos(A*X))/A",
|
|
"0",
|
|
|
|
"#293",
|
|
"integral(1/tan(A*X),X)-log(sin(A*X))/A",
|
|
"0",
|
|
|
|
"#294",
|
|
"integral(1/cos(A*X),X)-log(tan(pi/4+A*X/2))/A",
|
|
"0",
|
|
|
|
"#295",
|
|
"integral(1/sin(A*X),X)-log(tan(A*X/2))/A",
|
|
"0",
|
|
|
|
"#296",
|
|
"integral(sin(A*X)^2,X)-X/2+sin(2*A*X)/(4*A)",
|
|
"0",
|
|
|
|
"#297",
|
|
"integral(sin(A*X)^3,X)+cos(A*X)*(sin(A*X)^2+2)/(3*A)",
|
|
"0",
|
|
|
|
"#298",
|
|
"integral(sin(A*X)^4,X)-3/8*X+sin(2*A*X)/(4*A)-sin(4*A*X)/(32*A)",
|
|
"0",
|
|
|
|
"#302",
|
|
"integral(cos(A*X)^2,X)-X/2-sin(2*A*X)/(4*A)",
|
|
"0",
|
|
|
|
"#303",
|
|
"integral(cos(A*X)^3,X)-sin(A*X)*(cos(A*X)^2+2)/(3*A)",
|
|
"0",
|
|
|
|
"#304",
|
|
"integral(cos(A*X)^4,X)-3/8*X-sin(2*A*X)/(4*A)-sin(4*A*X)/(32*A)",
|
|
"0",
|
|
|
|
"#308",
|
|
"integral((1/sin(A*X))^2,X)+1/A*1/tan(A*X)",
|
|
"0",
|
|
|
|
"#312",
|
|
"integral((1/cos(A*X))^2,X)-tan(A*X)/A",
|
|
"0",
|
|
|
|
"#318",
|
|
"integral(sin(A*X)*cos(A*X),X)-sin(A*X)^2/(2*A)",
|
|
"0",
|
|
|
|
"#320",
|
|
"integral(sin(A*X)^2*cos(A*X)^2,X)+sin(4*A*X)/(32*A)-X/8",
|
|
"0",
|
|
|
|
"#326",
|
|
"integral(sin(A*X)/cos(A*X)/cos(A*X),X)-1/(A*cos(A*X))",
|
|
"0",
|
|
|
|
"#327",
|
|
"integral(sin(A*X)^2/cos(A*X),X)+sin(A*X)/A-log(tan(pi/4+A*X/2))/A",
|
|
"0",
|
|
|
|
"#328",
|
|
"integral(cos(A*X)/sin(A*X)^2,X)+1/(A*sin(A*X))",
|
|
"0",
|
|
|
|
"#329",
|
|
"integral(1/sin(A*X)/cos(A*X),X)-log(tan(A*X))/A",
|
|
"0",
|
|
|
|
"#330",
|
|
"integral(1/sin(A*X)/cos(A*X)^2,X)-(1/cos(A*X)+log(tan(A*X/2)))/A",
|
|
"0",
|
|
|
|
"#332",
|
|
"integral(1/sin(A*X)^2/cos(A*X),X)-(log(tan(pi/4+A*X/2))-1/sin(A*X))/A",
|
|
"0",
|
|
|
|
"#333",
|
|
"integral(1/sin(A*X)^2/cos(A*X)^2,X)+2/(A*tan(2*A*X))",
|
|
"0",
|
|
|
|
"#335",
|
|
"integral(sin(A+B*X),X)+cos(A+B*X)/B",
|
|
"0",
|
|
|
|
"#336",
|
|
"integral(cos(A+B*X),X)-sin(A+B*X)/B",
|
|
"0",
|
|
|
|
"#337+",
|
|
"integral(1/(1+sin(A*X)),X)+tan(pi/4-A*X/2)/A",
|
|
"0",
|
|
|
|
"#337b+",
|
|
"integral(1/(B+B*sin(A*X)),X)+tan(pi/4-A*X/2)/A/B",
|
|
"0",
|
|
|
|
"#337-",
|
|
"integral(1/(1-sin(A*X)),X)-tan(pi/4+A*X/2)/A",
|
|
"0",
|
|
|
|
"#337b-",
|
|
"integral(1/(B-B*sin(A*X)),X)-tan(pi/4+A*X/2)/A/B",
|
|
"0",
|
|
|
|
"#338",
|
|
"integral(1/(1+cos(A*X)),X)-tan(A*X/2)/A",
|
|
"0",
|
|
|
|
"#339",
|
|
"integral(1/(1-cos(A*X)),X)+1/(A*tan(A*X/2))",
|
|
"0",
|
|
|
|
"#340",
|
|
"integral(1/(A+B*sin(X)),X)-1/sqrt(B^2-A^2)*log((A*tan(X/2)+B-sqrt(B^2-A^2))/(A*tan(X/2)+B+sqrt(B^2-A^2)))",
|
|
"0",
|
|
|
|
"#341",
|
|
"integral(1/(A+B*cos(X)),X)-1/sqrt(B^2-A^2)*log((sqrt(B^2-A^2)*tan(X/2)+A+B)/(sqrt(B^2-A^2)*tan(X/2)-A-B))",
|
|
"0",
|
|
|
|
"#389",
|
|
"x*sin(A*x)-d(integral(x*sin(A*x)))",
|
|
"0",
|
|
|
|
"#390",
|
|
"x^2*sin(A*x)-d(integral(x^2*sin(A*x)))",
|
|
"0",
|
|
|
|
"#393",
|
|
"x*cos(A*x)-d(integral(x*cos(A*x)))",
|
|
"0",
|
|
|
|
"#394",
|
|
"x^2*cos(A*x)-d(integral(x^2*cos(A*x)))",
|
|
"0",
|
|
|
|
"#441",
|
|
"integral(arcsin(A*X),X)-X*arcsin(A*X)-sqrt(1-A^2*X^2)/A",
|
|
"0",
|
|
|
|
"#442",
|
|
"integral(arccos(A*X),X)-X*arccos(A*X)-sqrt(1-A^2*X^2)/A",
|
|
"0",
|
|
|
|
"#443",
|
|
"integral(arctan(A*X),X)-X*arctan(A*X)+log(1+A^2*X^2)/(2*A)",
|
|
"0",
|
|
|
|
"#485",
|
|
"integral(log(X),X)-X*log(X)+X",
|
|
"0",
|
|
|
|
"#485a",
|
|
"integral(log(A*X),X)-X*log(A*X)+X",
|
|
"0",
|
|
|
|
"#486",
|
|
"integral(X*log(X),X)-1/2*X^2*log(X)+1/4*X^2",
|
|
"0",
|
|
|
|
"#486a",
|
|
"integral(X*log(A*X),X)-1/2*X^2*log(A*X)+1/4*X^2",
|
|
"0",
|
|
|
|
"#487",
|
|
"integral(X^2*log(A*X),X)-1/3*X^3*log(A*X)+X^3/9",
|
|
"0",
|
|
|
|
"#489",
|
|
"integral(log(X)^2,X)-X*log(X)^2+2*X*log(X)-2*X",
|
|
"0",
|
|
|
|
"#493",
|
|
"integral(1/X*1/log(A*X),X)-log(log(A*X))",
|
|
"0",
|
|
|
|
"#499",
|
|
"integral(log(A*X+B),X)-(A*X+B)*log(A*X+B)/A+X",
|
|
"0",
|
|
|
|
"#500",
|
|
"integral(log(A*X+B)/X^2,X)-A*log(X)/B+(A*X+B)*log(A*X+B)/B/X",
|
|
"0",
|
|
|
|
"#554",
|
|
"integral(sinh(X),X)-cosh(X)",
|
|
"0",
|
|
|
|
"#555",
|
|
"integral(cosh(X),X)-sinh(X)",
|
|
"0",
|
|
|
|
"#556",
|
|
"integral(tanh(X),X)-log(cosh(X))",
|
|
"0",
|
|
|
|
"#560",
|
|
"integral(X*sinh(X),X)-X*cosh(X)+sinh(X)",
|
|
"0",
|
|
|
|
"#562",
|
|
"integral(X*cosh(X),X)-X*sinh(X)+cosh(X)",
|
|
"0",
|
|
|
|
"#566",
|
|
"integral(sinh(X)^2,X)-sinh(2*X)/4+X/2",
|
|
"0",
|
|
|
|
"#569",
|
|
"integral(tanh(X)^2,X)-X+tanh(X)",
|
|
"0",
|
|
|
|
"#572",
|
|
"integral(cosh(X)^2,X)-sinh(2*X)/4-X/2",
|
|
"0",
|
|
|
|
// test integral(exp(a*x^2))
|
|
|
|
"integral(exp(a*x^2))+i*sqrt(pi)*erf(i*sqrt(a)*x)/sqrt(a)/2",
|
|
"0",
|
|
|
|
"integral(exp(-x^2))-sqrt(pi)*erf(x)/2",
|
|
"0",
|
|
|
|
"integral(exp(-3*x^2))-sqrt(pi/3)*erf(sqrt(3)*x)/2",
|
|
"0",
|
|
|
|
"integral(1/x*1/(a+log(x)),x)-log(a+log(x))",
|
|
"0",
|
|
|
|
"integral(exp(a*x+b*x))",
|
|
"exp((a+b)*x)/(a+b)",
|
|
|
|
"integral(x*exp(a*x))",
|
|
"-exp(a*x)/(a^2)+x*exp(a*x)/a",
|
|
"derivative",
|
|
"x*exp(a*x)",
|
|
|
|
"integral(x*exp(a*x+b))",
|
|
"-exp(a*x+b)/(a^2)+x*exp(a*x+b)/a",
|
|
"derivative",
|
|
"x*exp(a*x+b)",
|
|
|
|
"integral(x*exp(-a*x+b))",
|
|
"-exp(-a*x+b)/(a^2)-x*exp(-a*x+b)/a",
|
|
"derivative",
|
|
"x*exp(-a*x+b)",
|
|
|
|
"integral(x^2*exp(a*x))",
|
|
"2*exp(a*x)/(a^3)-2*x*exp(a*x)/(a^2)+x^2*exp(a*x)/a",
|
|
"derivative",
|
|
"x^2*exp(a*x)",
|
|
|
|
"integral(x^2*exp(a*x+b))",
|
|
"2*exp(a*x+b)/(a^3)-2*x*exp(a*x+b)/(a^2)+x^2*exp(a*x+b)/a",
|
|
"derivative",
|
|
"x^2*exp(a*x+b)",
|
|
|
|
"integral(x^3*exp(a*x))",
|
|
"-6*exp(a*x)/(a^4)+6*x*exp(a*x)/(a^3)-3*x^2*exp(a*x)/(a^2)+x^3*exp(a*x)/a",
|
|
"derivative",
|
|
"x^3*exp(a*x)",
|
|
|
|
"integral(x^3*exp(a*x+b))",
|
|
"-6*exp(a*x+b)/(a^4)+6*x*exp(a*x+b)/(a^3)-3*x^2*exp(a*x+b)/(a^2)+x^3*exp(a*x+b)/a",
|
|
"derivative",
|
|
"x^3*exp(a*x+b)",
|
|
|
|
"integral(sqrt(a*x^2+b))",
|
|
"Stop: integral: sorry, could not find a solution",
|
|
|
|
"integral(x^2*(1-x^2)^(3/2))-(x*sqrt(1-x^2)*(-8*x^4+14*x^2-3)+3*arcsin(x))/48",
|
|
"0",
|
|
|
|
"integral(x^4*(1-x^2)^(3/2))-(-x*sqrt(1-x^2)*(16*x^6-24*x^4+2*x^2+3)+3*arcsin(x))/128",
|
|
"0",
|
|
|
|
"integral(x^2*(1-x^2)^(5/2))-(x*sqrt(1-x^2)*(48*x^6-136*x^4+118*x^2-15)+15*arcsin(x))/384",
|
|
"0",
|
|
};
|
|
|
|
void
|
|
test_integral(void)
|
|
{
|
|
test(__FILE__, s, sizeof s / sizeof (char *));
|
|
}
|
|
|
|
#endif
|