Prove that `int_(0)^(pi/2)sin2xlogtanxdx=0`

Find the value of int_(0)^(pi//2)sin2xlogtanxdx .

Prove that int_0^(pi/2)sin^3xdx=2/3

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

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

int_(0)^(pi/4) sin 2x dx

Prove that : int_(0)^(pi//2) (sin x-cos x)/(1+sin x cos x)dx=0 " (ii) Prove that " : int_(0)^(pi//2) sin 2x. log (tan-x) dx=0

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

Prove that int_(0)^(pi/2) sin^(3) x dx=(2)/(3)

Prove that : int_(0)^(pi//2) x . cot x dx =(pi)/(2)log 2

int_0^(pi/2) sin^2xcos^2xdx