Primitive of Hyperbolic Cosecant Function
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Theorem
Logarithm Form
- $\ds \int \csch x \rd x = -\ln \size {\csch x + \coth x} + C$
where $\csch x + \coth x \ne 0$.
Hyperbolic Tangent Form
- $\ds \int \csch x \rd x = \ln \size {\tanh \frac x 2} + C$
where $\tanh \dfrac x 2 \ne 0$.
Inverse Hyperbolic Cotangent Form
- $\ds \int \csch x \rd x = -2 \map {\coth^{-1} } {e^x} + C$
Inverse Hyperbolic Cotangent of Hyperbolic Cosine Form
- $\ds \int \csch x \rd x = -\map {\coth^{-1} } {\cosh x} + C$