Difference between revisions of "Antiderivative of arcsin"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\displaystyle\int \mathrm{arcsin}(z)...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\displaystyle\int \mathrm{arcsin}(z) \mathrm{d}z = \sqrt{1-z^2}+z\mathrm{arcsin}(z)+C,$$ | $$\displaystyle\int \mathrm{arcsin}(z) \mathrm{d}z = \sqrt{1-z^2}+z\mathrm{arcsin}(z)+C,$$ | ||
where $\mathrm{arcsin}$ denotes the [[arcsin|inverse sine]] function. | where $\mathrm{arcsin}$ denotes the [[arcsin|inverse sine]] function. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | [[Category:Theorem]] | |
Revision as of 07:21, 8 June 2016
Theorem
The following formula holds: $$\displaystyle\int \mathrm{arcsin}(z) \mathrm{d}z = \sqrt{1-z^2}+z\mathrm{arcsin}(z)+C,$$ where $\mathrm{arcsin}$ denotes the inverse sine function.
