" Prove that "int_(0)^( pi/2)log sin xdx=-(pi)/(2)log2

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

int_(0)^( pi)log xdx

Prove that int_(0)^(pi/4)log(1+tanx)dx=(pi)/(8) log2.

int_(0)^(pi)log sin^(2)x dx=

Show that int_(0)^((pi)/(2))log(sin2x)dx=-(pi)/(2)(log2)

Statement-1: int_(0)^(pi//2) x cot x dx=(pi)/(2)log2 Statement-2: int_(0)^(pi//2) log sin x dx=-(pi)/(2)log2

Evaluate int_(0)^( pi)x log sin xdx

int_ (0) ^ (pi) x log sin xdx

Evaluate int_0^(pi/2) log sin xdx