int_(1-x+cos x)^( pi/2)(sin^(3)x)/(sin x+x)=

Prove that int_(0)^((pi)/(2))(sin^(2)x)/(1+sin x cos x)dx=(pi)/(3sqrt(3))

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

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

int_(pi//6)^(pi//3) (sin^(3) x)/(sin^(3) x + cos^(3) x) dx=

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

What is int_(0)^(pi//2) (sin^(3)x)/(sin^(3)x + cos^(3)x) dx ?

int_(-pi//2)^(pi//2)(sin^(4)x)/(sin^(4)x + cos^(4)x)dx=

int_(-pi//2)^(pi//2)(sin^(2)x.cos^(2)x(sin x+cos 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: