Mathematics

Solve: $$\displaystyle\int\dfrac {\sin^{-1}x}{\sqrt {1-x^{2}}}$$


SOLUTION
$$Let, I = \displaystyle\int \dfrac{\sin^{-1} x}{\sqrt{1 - x^2}} dx$$

Put                  $$ \sin^{-1} x = t $$

$$\implies \dfrac{1}{\sqrt{1 - x^2}} dx = dt $$

$$\therefore I = \int t dt$$

$$ I = \dfrac{t^{2}}{2} + c = \dfrac{(\sin^{-1} x)^{2} }{2}+ c$$ (Ans)
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Subjective Medium Published on 17th 09, 2020
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