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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