`int_-pi^pi (x(1+sin x))/(1+cos^(2)x)dx`

Evaluate int_(-pi)^( pi)(2x(1+sin x))/(1+cos^(2)x)dx, state the relevant properties used.

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

Evaluate (i) int_0^pi (x sin x)/(1+cos^2 x) dx Evaluate (ii) int_0^pi (4x sin x)/(1+ cos^2 x) dx

Evaluate: int_(-pi)^( pi)((2x)(1+sin x)/(1+cos^(2)x))dx

int_(0)^( pi)(sin x)/(1+cos^(2)x)dx =

int_(-pi)^(pi)(1-x^(2))sin x cos^(2)x dx=

If I_(1) = int_(0)^(pi) (x sin x)/(1+cos^2x) dx , I_(2) = int_(0)^(pi) x sin^(4)xdx then, I_(1) : I_(2) is equal to

The value of int_(-pi)^(pi)(1-x^(2)) sin x cos^(2) x" dx" , is