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
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: Integrals involving $\coth a x$: $14.620$