int(sin x)/((1+cos x)^(2))dx=4 pi

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

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

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

int_ (0) ^ ((pi) / (2)) (sin x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (cos x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (dx) / (1 + cot x) = int_ (0) ^ ((pi) / (2)) (dx) / ( 1 + time x) = (pi) / (4)

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 int_(0)^((pi)/(2))(dx)/(1+sin x+cos x)=In2, then the value of int_(0)^((pi)/(2))(sin x)/(1+sin x+cos x)dx is equal to: