`I=int_(0)^( pi)(x sin^(3)x)/((1+cos^(2)x)dx`

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

int_(0)^( pi)((x)/(1+sin^(2)x)+cos^(3)x)dx

If I_(1)=int_(0)^( pi)xf(sin^(3)x+cos^(2)x)dx and I_(2)=int_(0)^((pi)/(2))f(sin^(3)x+cos^(2)x)dx, then relate I_(1) and I_(2)

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

If I_(1)=int_(0)^((pi)/(2))(cos^(2)x)/(1+cos^(2)x)dx,I_(2)=int_(0)^((pi)/(2))(sin^(2)x)/(1+sin^(2)x)dxI_(3)=int_(0)^((pi)/(2))(1+2cos^(2)x sin^(2)x)/(4+2cos^(2)x sin^(2)x)dx, then I_(1)=I_(2)>I_(3)(b)I_(3)>I_(1)=I_(2)I_(1)=I_(2)=I_(3)(d) none of these

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

int_(0)^( pi)( sin x*cos^(3)x)dx

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