`I= int_0^(pi)(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 =

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)(sin x)/(1+cos x)dx

Prove that int_0^a f(x)dx=int_0^af(a-x)dx , hence evaluate int_0^pi(x sin x)/(1+cos^2 x)dx

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

Evaluate the following integral: int_0^(pi//2)(sin^2x)/((1+cos x)^2)dx