Primitive of Hyperbolic Cosecant Function

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

$\ds \int \csch x \rd x = -\map {\coth^{-1} } {\cosh x} + C$

Also see

• Primitive of Hyperbolic Sine Function
• Primitive of Hyperbolic Cosine Function

• Primitive of Hyperbolic Tangent Function
• Primitive of Hyperbolic Cotangent Function

• Primitive of Hyperbolic Secant Function

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: General Rules of Integration: $14.30$
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 16$: Indefinite Integrals: General Rules of Integration: $16.30.$