Difference between revisions of "Antiderivative of coth"
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| − | <strong>Theorem:</strong> The following formula holds: | + | <strong>[[Antiderivative of coth|Theorem]]:</strong> The following formula holds: |
$$\displaystyle\int \mathrm{coth}(z)dz=\log(\sinh(z)),$$ | $$\displaystyle\int \mathrm{coth}(z)dz=\log(\sinh(z)),$$ | ||
where $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]], $\log$ denotes the [[logarithm]], and $\sinh$ denotes the [[sinh|hyperbolic sine]]. | where $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]], $\log$ denotes the [[logarithm]], and $\sinh$ denotes the [[sinh|hyperbolic sine]]. | ||
Revision as of 05:40, 16 May 2015
Theorem: The following formula holds: $$\displaystyle\int \mathrm{coth}(z)dz=\log(\sinh(z)),$$ where $\mathrm{coth}$ denotes the hyperbolic cotangent, $\log$ denotes the logarithm, and $\sinh$ denotes the hyperbolic sine.
Proof: █
