int_(pi/4)^( pi/2)cos2x*log sin xdx

int_(0)^((pi)/(2))cos2x log sin xdx

int_(pi//4)^(pi//2) cos 2 x log sin x " " dx=

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

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

Evaluate int_(0)^((pi)/(2))log sin xdx

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

Prove that int_(-pi/4)^( pi/4)log(sin x+cos x)backslash dx=-(pi)/(4)backslash log2

[int_(-pi/4)^( pi/4)log(cos x+sin x)dx=(1)/(2)],[[" 1) "pi log2," 2) "-pi log2," 3) "-(pi)/(4)log2," 4) "-(pi)/(2)log2]]

Show that: int_(0)^( pi/2)f(sin2x)sin xdx=sqrt(2)int_(0)^( pi/4)f(cos2x)cos xdx

int_(0)^(pi/2)cos^2x sin^2xdx