Difference between revisions of "Antiderivative of arcsin"

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==Theorem==
<strong>[[Antiderivative of arcsin|Theorem]]:</strong> The following formula holds:
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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.
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<strong>Proof:</strong> █
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==Proof==
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[[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.

Proof