Primitive of Reciprocal of Hyperbolic Cotangent of a x

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Theorem

$\ds \int \frac {\d x} {\coth a x} = \frac {\ln \size {\cosh a x} } a + C$


Proof

\(\ds \int \frac {\d x} {\coth a x}\) \(=\) \(\ds \int \tanh a x \rd x\) Hyperbolic Cotangent is Reciprocal of Hyperbolic Tangent
\(\ds \) \(=\) \(\ds \frac {\ln \size {\cosh a x} } a + C\) Primitive of $\tanh a x$

$\blacksquare$


Also see


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