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Question Number 91004 by jagoll last updated on 27/Apr/20

$$\int \tan \left(arc\sin x\right)dx$$

Commented by jagoll last updated on 27/Apr/20

$$let{\sin }^{-1}\left(x\right)=y\Rightarrow x=\sin y$$$$dx=\cos ydy$$$$\tan \left({\sin }^{-1}\left(x\right)\right)=\tan y$$$$\int \tan \left(y\right)\cos \left(y\right)dy=$$$$\int \sin \left(y\right)dy=-\cos y+c$$$$=-\sqrt{1-x^2}+c$$

Commented by MJS last updated on 27/Apr/20

$$\tan \arcsin x=\frac{x}{\sqrt{1-x^2}}$$$$\mathrm{anyway}\mathrm{your}\mathrm{path}\mathrm{is}\mathrm{right}$$

Commented by jagoll last updated on 27/Apr/20

$$wawyouaregreatsir...$$$$thankyou$$

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