int_(0)^((pi)/(2))(dx^(2))/(4+5cos x)=(1)/(3)log2

int_(0)^((pi)/(2))(dx)/(4+5cosx)=(1)/(3)log2

int_(0)^((pi)/(2))(1)/(4+5cos x)dx=

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

Given int_(0)^((pi)/(2))(dx)/(1+sin x+cos x)=log2. Then the value of integral int_(0)^((pi)/(2))(sin x)/(1+sin x+cos x)dx is equal to (1)/(2)log2(b) is (pi)/(2)-log2(pi)/(4)-(1)/(2)log2(d)(pi)/(2)+log2

int_(0)^((pi)/(2))log(sinx)dx=int_(0)^((pi)/(2))log(cosx)dx=(pi)/(2)log.(1)/(2)

int_(0)^((pi)/(2))log(sinx)dx=int_(0)^((pi)/(2))log(cosx)dx=(pi)/(2)log.(1)/(2)

int_(0)^((pi)/(2))log sin xdx=int_(0)^((pi)/(2))log cos xdx=(1)/(2)(pi)log((1)/(2))

int_(0)^((pi)/(2))log(cos x)dx=