Difference between revisions of "Antiderivative of hyperbolic cosecant"

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==Theorem==
<strong>[[Antiderivative of hyperbolic cosecant|Theorem]]:</strong> The following formula holds:
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The following formula holds:
$$\displaystyle\int \mathrm{csch}(z)dz = \log\left(\tanh\left(\frac{z}{2}\right)\right),$$
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$$\displaystyle\int \mathrm{csch}(z)\mathrm{d}z = \log\left(\tanh\left(\frac{z}{2}\right)\right)+C,$$
 
where $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]], $\log$ denotes the [[logarithm]], and $\tanh$ denotes the [[tanh|hyperbolic tangent]].
 
where $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]], $\log$ denotes the [[logarithm]], and $\tanh$ denotes the [[tanh|hyperbolic tangent]].
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<strong>Proof:</strong> █
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==Proof==
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==References==
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 07:55, 8 June 2016

Theorem

The following formula holds: $$\displaystyle\int \mathrm{csch}(z)\mathrm{d}z = \log\left(\tanh\left(\frac{z}{2}\right)\right)+C,$$ where $\mathrm{csch}$ denotes the hyperbolic cosecant, $\log$ denotes the logarithm, and $\tanh$ denotes the hyperbolic tangent.

Proof

References