" Prove that "int_(0)^( pi/2)log(sin x)dx

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

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

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

Prove that: int_(0)^( pi/2)log(sin^(3)x cos^(4)x)backslash dx=-(7 pi)/(2)log2

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

int_(0)^( pi/2)ln(sin^(2)x cos x)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) .

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