Primitive of Inverse Hyperbolic Cotangent Function

Theorem

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

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

The result follows by setting $a = 1$.

Also see

 * Primitive of $\arsinh x$
 * Primitive of $\arcosh x$
 * Primitive of $\artanh x$