Difference between revisions of "Antiderivative of coth"
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<strong>[[Antiderivative of coth|Theorem]]:</strong> The following formula holds: | <strong>[[Antiderivative of coth|Theorem]]:</strong> The following formula holds: | ||
| − | $$\displaystyle\int \mathrm{coth}(z) \mathrm{d}z=\log(\sinh(z)),$$ | + | $$\displaystyle\int \mathrm{coth}(z) \mathrm{d}z=\log(\sinh(z)) + C,$$ |
| − | 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]]. |
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<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
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Revision as of 22:43, 30 May 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.
Proof: █
