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

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

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

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

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

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

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(sin x-cos x)/(1+sin x cos x)dx

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

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

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