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Question Number 127110 by benjo_mathlover last updated on 26/Dec/20

$$\int {\left(\arcsin x\right)}^{2}dx=?$$

Answered by liberty last updated on 27/Dec/20

$$letting\arcsin x=\ell \Rightarrow x=\sin \ell \wedge dx=\cos \ell d\ell$$$$I=\int {\ell }^2\cos \ell d\ell ={\ell }^2\sin \ell +2\ell \cos \ell -2\sin \ell +c$$$$=x{\left(\arcsin x\right)}^2+2\sqrt{1-x^2}\arcsin x-2x+c$$$$$$

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