Difference between revisions of "Antiderivative of sech"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\displaystyle\int \mathrm{sech}(z) \mathrm{d}z=\arctan(\sinh(z)) + C,$$ | $$\displaystyle\int \mathrm{sech}(z) \mathrm{d}z=\arctan(\sinh(z)) + C,$$ | ||
where $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]], $\arctan$ denotes the [[arctan|inverse tangent]], and $\sinh$ denotes the [[sinh|hyperbolic sine]]. | where $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]], $\arctan$ denotes the [[arctan|inverse tangent]], and $\sinh$ denotes the [[sinh|hyperbolic sine]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:05, 9 June 2016
Theorem
The following formula holds: $$\displaystyle\int \mathrm{sech}(z) \mathrm{d}z=\arctan(\sinh(z)) + C,$$ where $\mathrm{sech}$ denotes the hyperbolic secant, $\arctan$ denotes the inverse tangent, and $\sinh$ denotes the hyperbolic sine.
