Primitive of Function of Arccotangent

Theorem

 * $\displaystyle \int F \left({\operatorname{arccot} \frac x a}\right) \ \mathrm d x = -a \int F \left({u}\right) \csc^2 u \ \mathrm d u$

where $u = \operatorname{arccot} \dfrac x a$.

Proof
First note that:

Then: