Primitive of Arccotangent Function

Theorem

 * $\ds \int \arccot x \rd x = x \arccot x + \frac {\map \ln {x^2 + 1} } 2 + C$

Proof
From Primitive of $\arccot \dfrac x a$:
 * $\ds \int \arctan \frac x a \rd x = x \arccot \frac x a + \frac a 2 \map \ln {x^2 + a^2} + C$

The result follows by setting $a = 1$.

Also see

 * Primitive of $\arcsin x$
 * Primitive of $\arccos x$
 * Primitive of $\arctan x$