Difference between revisions of "Antiderivative of sech"
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<strong>[[Antiderivative of sech|Theorem]]:</strong> The following formula holds: | <strong>[[Antiderivative of sech|Theorem]]:</strong> The following formula holds: | ||
| − | $$\displaystyle\int \mathrm{sech}(z) | + | $$\displaystyle\int \mathrm{sech}(z) \mathrm{d}z=\arctan(\sinh(z)),$$ |
where $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]], $\arctan$ denotes the [[arctan|inverse tangent]], and $\sinh$ denotes the [[sinh|hyperbolic sine]]. | where $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]], $\arctan$ denotes the [[arctan|inverse tangent]], and $\sinh$ denotes the [[sinh|hyperbolic sine]]. | ||
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Revision as of 08:29, 16 May 2016
Theorem: The following formula holds: $$\displaystyle\int \mathrm{sech}(z) \mathrm{d}z=\arctan(\sinh(z)),$$ where $\mathrm{sech}$ denotes the hyperbolic secant, $\arctan$ denotes the inverse tangent, and $\sinh$ denotes the hyperbolic sine.
Proof: █
