`3. int_(0)^( pi/2)( sin2 x)/(1+cos^(2)x)dx`

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

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

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

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

Evaluate int_(-pi/2)^(pi/2)(sin2x)/(1+cos^3x)dx

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

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

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

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