Evaluate integral of sqrt(cot(theta)) d(theta) over the limits (0 to pi/2) by expressing in terms of gamma function

Question

Show that integral of d(theta)/sqrt(sin(theta)) for limits (0 to pi/2) multiplied by integral of sqrt(sin(theta)) d(theta) equals to pi
Evaluate integral of sqrt(cot(theta)) d(theta) over the limits (0 to pi/2) by expressing in terms of gamma function
Evaluate integral of (4-x^2)^(3/2) dx over the limits (0 to 2)
Evaluate integral of (1/(1+x^4)) dx over the limits (0 to infinity)
Show that beta(m,n) = integral of (x^(m-1)/(1+x)^(m+n)) dx over the limits (0 to infinity)