Answer
$-\frac{2(cot(x))^{3/2}}{3} +C$
Work Step by Step
Evaluate the Integral using substitution: $\int \sqrt{cot(x)}csc^2(x)dx$
Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$
$u= cot(x)$
$du =-csc^2(x)$
Since $du$ in the expression is equal to $(csc^2(x))$ it must be multiplied by $-1$
Solve the integral in terms of $u$:
$\int \sqrt{u}(-1)du$
$-1\int \sqrt{u}du $
$-\frac{2(u)^{3/2}}{3}+C$
Substitute for $u$:
$-\frac{2(cot(x))^{3/2}}{3} +C$
