Primitive of Hyperbolic Cosecant Function/Inverse Hyperbolic Cotangent Form/Mistake

Source Work

 * Chapter $14$: Indefinite Integrals
 * General Rules of Integration: $14.30$

This mistake can be seen in the edition as published by Schaum: ISBN 0-07-060224-7 (unknown printing).

Mistake

 * $\displaystyle \int \operatorname{csch} u \ \mathrm d u = - \coth^{-1} \left({e^u}\right) + C$

As demonstrated in Primitive of Hyperbolic Cosecant Function: Inverse Hyperbolic Cotangent Form the correct expression is in fact:


 * $\displaystyle \int \operatorname{csch} u \ \mathrm d u = -2 \coth^{-1} \left({e^u}\right) + C$