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 Q23  Integrate the functions \frac{\sin ^{-1}x}{\sqrt { 1- x^2 }}

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Given function  \frac{\sin ^{-1}x}{\sqrt { 1- x^2 }},

Assume the \sin^{-1}x =t

 \therefore \frac{1}{\sqrt{1-x^2}}dx = dt

\implies \int \frac{\sin^{-1}x}{\sqrt{1-x^2}}dx =\int t dt

= \frac{t^2}{2}+C                      

Now, back substituted the value of t.

= \frac{(\sin^{-1}x)^2}{2}+C, where C is any constant value.

Posted by

Divya Prakash Singh

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