Evaluate `int_(0)^(pi//2) (sqrt(cot x))/(sqrt(cot x) + sqrt(tan x)) dx.`

Evaluate int_(0)^(pi//2) (sqrt( sin x))/(sqrt(sin x)+ sqrt(cos x))dx.

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

Evaluate int_(0)^(pi//2) (cos^(5) x)/(sin^(5)x + cos^(5) x) dx.

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a-x) dx . Hence, evaluate int_(0)^(pi//2) (sin x - cos x)/(1+ sin x cos x) dx.

Evaluate int_(0)^(pi//2) (sin^(3//2)x)/(sin^(3//2)x+ cos^(3//2) x)dx