Difference between revisions of "Antiderivative of tanh"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\displaystyle\int \tanh(z)dz = \log(\c...") |
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<strong>[[Antiderivative of tanh|Theorem]]:</strong> The following formula holds: | <strong>[[Antiderivative of tanh|Theorem]]:</strong> The following formula holds: | ||
| − | $$\displaystyle\int \tanh(z) | + | $$\displaystyle\int \tanh(z)\mathrm{d}z = \log(\cosh(z)),$$ |
where $\tanh$ denotes the [[tanh|hyperbolic tangent]], $\log$ denotes the [[logarithm]], and $\cosh$ denotes the [[cosh|hyperbolic cosine]]. | where $\tanh$ denotes the [[tanh|hyperbolic tangent]], $\log$ denotes the [[logarithm]], and $\cosh$ denotes the [[cosh|hyperbolic cosine]]. | ||
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Revision as of 08:13, 16 May 2016
Theorem: The following formula holds: $$\displaystyle\int \tanh(z)\mathrm{d}z = \log(\cosh(z)),$$ where $\tanh$ denotes the hyperbolic tangent, $\log$ denotes the logarithm, and $\cosh$ denotes the hyperbolic cosine.
Proof: █
