int_(0)^( pi/4)log sin2xdx=-(pi)/(4)log2

int_(0)^( pi)log xdx

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

Show that int_(0)^((pi)/(2))logsinxdx=(pi)/(2)log((1)/(2))=(-pi)/(2)log2

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/4)sin^(4)xdx

int_(0)^( pi/4)sin2x*sin3xdx

int_(0)^( pi/4)sin2x sin3xdx

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