`int_0^(pi) (x+sin x)/(1+ cos x) dx`

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

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

I= int_0^(pi)(x sin x)/(1+cos^(2)x)dx

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

int_(0)^(pi)(x sin x)/(1-sin x)dx=

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

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

The value of the integral int_(0)^(pi) (x sin x)/(1+cos^(2)x)dx , is

The value of int_(0)^(pi//2) (x+sin x)/(1+cos x)dx , is