" 22."int_(0)^( pi)(sin x)/(sin x+cos x)dx

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

int_(0)^((pi)/(2))(x)/(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

int_(0)^( pi)(1)/(1+(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:

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

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

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

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