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Question Number 36752 by prof Abdo imad last updated on 05/Jun/18

$$find\int \frac{dx}{arcsinx\sqrt{1-x^2}}.$$

Commented by tanmay.chaudhury50@gmail.com last updated on 05/Jun/18

$$isit\int \frac{dx}{{sin}^{-1}\left(x\sqrt{1-x^2}\right)}plsclarify$$

Commented by abdo.msup.com last updated on 05/Jun/18

$$find\int \frac{dx}{\sqrt{1-x^2}arcsin\left(x\right)}$$

Commented by tanmay.chaudhury50@gmail.com last updated on 05/Jun/18

$$ok...sir$$

Commented by prof Abdo imad last updated on 06/Jun/18

$$changementx=sin\theta give$$$$I=\int \frac{cos\theta d\theta }{\theta cos\theta }=\int \frac{d\theta }{\theta }=ln\mid \theta \mid +c$$$$I=ln\mid arcsin\left(x\right)\mid +c.$$

Answered by tanmay.chaudhury50@gmail.com last updated on 05/Jun/18

$$\int \frac{dx}{\left(\sqrt{1-x^2}\right){sin}^{-1}x}$$$$t={sin}^{-1}x$$$$x=sint$$$$dx=costdt$$$$\int \frac{costdt}{\sqrt{1-{sin}^{2}t}\times t}$$$$\int \frac{dt}{t}=lnt+c$$$$=ln\mid \left({sin}^{-1}x\right)\mid +c$$

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