(1)/((1+tan^(3)x)^(2))

int_(0)^(1) ((tan^(-1)x)^(3))/(1+x^(2))dx=

The integral int(sin^(2)x cos^(2)x)/((sin^(5)x+cos^(3)x sin^(2)x+sin^(3)x cos^(2)x+cos^(5)x)^(2))dx is equal to (1) (1)/(3(1+tan^(3)x))+C(2)(-1)/(3(1+tan^(3)x))+C(3)(1)/(1+cot^(3)x)+C(4)(-1)/(1+cot^(3)x)+C

int(x^(4)+1)/(x^(6)+1)dx(1)tan^(-1)x-tan^(-1)x^(3)+c(2)tan^(-1)x-(1)/(3)tan^(-1)x^(3)+c(3)tan^(-1)x+tan^(-1)x^(3)+c(4)tan^(-1)x+(1)/(3)tan^(-1)x^(3)+c

prove that int(x^(2))/((x^(2)+1)(x^(2)+4))dx=-(1)/(3)tan^(-1)x+(2)/(3)tan^(-1)((x)/(2))+

2 tan ( tan^(-1)(x)+ tan^(-1)(x^(3))) " where " x in R - {-1,1} is equal to

2 tan ( tan^(-1)(x)+ tan^(-1)(x^(3))) " where " x in R - {-1,1} is equal to

Prove that tan^(-1)""(3a^(2)x-x^(3))/(a^(3)-3ax^(2))=3tan^(-1)""x/a .

Prove that tan(2tan^(-1)x)=2tan(tan^(-1)x+tan^(-1)x^(3))

int_(1//sqrt3)^(1)(Tan^(-1)x)^(3)/(1+x^(2))dx=