" 44.Prove that "int_(0)^((pi)/(2))log(sin x)dx=-(pi)/(2)log_(e)2

int_(0)^((pi)/(2))log(sin2x)dx

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

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

int_(0)^( pi)cos2x*log(sin x)dx

Prove that int_(0)^((pi)/(2)) log ( tan x ) dx = 0

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

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

Prove that int_(0)^(pi//2)(2logsinx-logsin2x)dx=(pi)/(2)(log2) .

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

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) .