" (a) "int_(0)^(4)(sin x)/(1+sin x cos x)dx

Examples: int_(0)^((pi)/(4))(sin x)/(sin x+cos x)dx

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

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)(1)/(1+(sin x)^(cos x))dx

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

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

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

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

Evaluate the following : int_(0)^(pi//4)(sin 2x)/(sin^(4)x+cos^(4)x)dx.