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

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

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

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

int_(0)^(pi) x sin x cos^(2)x\ dx

int_(0)^(pi) x sin x. cos^(2) x dx

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

int_(0)^((pi)/(2))(x sin x*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