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

Show that : int_(0)^((pi)/(2))(sin^(2)x)/(sin x+cos x)dx=(1)/(sqrt(2))log(sqrt(2)+1)

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

Prove that int_0^(pi/2) \ sin^2 x / (1+sin x cos x) \ dx = pi/(3 sqrt(3)

Prove that : int_(0)^(pi//2) (sin^(3)x)/(sin^(3) x+ cos^(3)x)dx =(pi)/(4)

Prove that : int_(0)^(pi//2) (sin^(3)x)/(sin^(3) x+ cos^(3)x)dx =(pi)/(4)

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3)x)/(sin^(3)x+cos^(3)x)dx=(pi)/4

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

int_(0)^( pi)sin^(3)x(1+2cos x)(1+cos x)^(2)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:

int_(0)^(pi//2) (Cos x)/(1+Sin x) dx=