" 31.(i) "int_(0)^((pi)/(2))(dx)/(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) (1)/(4+3 cos x)dx

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

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

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

Evaluate int_(0)^(pi"/"2) (dx)/(4 + 5 cos x)

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

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

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .