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,$$ | ||
| − | where $\mathrm{arcsin}$ | + | where $\mathrm{arcsin}$ [[arcsin]]. |
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 22:45, 28 March 2017
Theorem
The following formula holds: $$\displaystyle\int \mathrm{arcsin}(z) \mathrm{d}z = \sqrt{1-z^2}+z\mathrm{arcsin}(z)+C,$$ where $\mathrm{arcsin}$ arcsin.
