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

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

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

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

Evaluate the integrals int_(0)^((pi)/(2))(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)

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

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

int_(0)^( pi/4)(1+sin2x)/(cos x+sin 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