Primitive of Product of Hyperbolic Cosecant and Cotangent
Jump to navigation
Jump to search
Theorem
- $\ds \int \csch x \coth x \rd x = -\csch x + C$
where $C$ is an arbitrary constant.
Proof
From Derivative of Hyperbolic Cosecant:
- $\dfrac \d {\d x} \csch x = -\csch x \coth x$
The result follows from the definition of primitive.
$\blacksquare$
Sources
- 1960: Margaret M. Gow: A Course in Pure Mathematics ... (previous) ... (next): Chapter $10$: Integration: $10.4$. Standard integrals: Other Standard Results: $\text {(xxxii)}$
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: General Rules of Integration: $14.38$
- 1974: Murray R. Spiegel: Theory and Problems of Advanced Calculus (SI ed.) ... (previous) ... (next): Chapter $5$. Integrals: Integrals of Special Functions: $24$