Difference between revisions of "Antiderivative of arcsin"
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The following formula holds: | 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== | ==Proof== | ||
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[[Category:Theorem]] | [[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.
