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

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(2log sin x-log sin2x)dx

int_(0)^((pi)/(2))(2log cos x-log sin2x)dx

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

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

Prove that int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx and hence evaluate int_(0)^(pi//2)(2log sin x-log sin2x)dx .

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

Evaluate: \int_{0}^(pi/2) (2 log sinx - log sin 2x) dx

Evaluate : int_0^(pi/2) (2 log cos x-log sin 2x)dx .

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

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