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

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Source Work

1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables

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).


$\displaystyle \int \csch u \rd u = -\map {\coth^{-1} } {e^u} + C$

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

$\displaystyle \int \csch u \rd u = -2 \, \map {\coth^{-1} } {e^u} + C$