Difference between revisions of "Antiderivative of tanh"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\displaystyle\int \tanh(z)\mathrm{d}z = \log(\cosh(z)),$$ | $$\displaystyle\int \tanh(z)\mathrm{d}z = \log(\cosh(z)),$$ | ||
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]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 00:03, 17 June 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.
