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).
Mistake
- $\ds \int \csch u \rd u = -\map {\coth^{-1} } {e^u} + C$
As demonstrated in Primitive of Hyperbolic Cosecant Function: Inverse Hyperbolic Cotangent Form the correct expression is in fact:
- $\ds \int \csch u \rd u = -2 \map {\coth^{-1} } {e^u} + C$