Prove

Question:

$\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}$

Solution:

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

$\therefore \frac{1}{\sqrt{1-x^{2}}} d x=d t$

$\Rightarrow \int \frac{\sin ^{-1} x}{\sqrt{1-x^{2}}} d x=\int t d t$

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

$=\frac{\left(\sin ^{-1} x\right)^{2}}{2}+\mathrm{C}$

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