Difference between revisions of "Antiderivative of coth"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\displaystyle\int \mathrm{coth}(z) \mathrm{d}z=\log(\sinh(z)) + C,$$ | $$\displaystyle\int \mathrm{coth}(z) \mathrm{d}z=\log(\sinh(z)) + C,$$ | ||
for arbitrary constant $C$, where $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]], $\log$ denotes the [[logarithm]], and $\sinh$ denotes the [[sinh|hyperbolic sine]]. | for arbitrary constant $C$, where $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]], $\log$ denotes the [[logarithm]], and $\sinh$ denotes the [[sinh|hyperbolic sine]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 03:54, 17 June 2016
Theorem
The following formula holds: $$\displaystyle\int \mathrm{coth}(z) \mathrm{d}z=\log(\sinh(z)) + C,$$ for arbitrary constant $C$, where $\mathrm{coth}$ denotes the hyperbolic cotangent, $\log$ denotes the logarithm, and $\sinh$ denotes the hyperbolic sine.
