Question

Integrate the following functions.
$\int \frac{si{n}^{-1}x}{\sqrt{1-x^2}}dx.$

Answer 1

Let I = $\int \frac{si{n}^{-1}x}{\sqrt{1-x^2}}dx.$
Let $si{n}^{-1}x=t$
$\Rightarrow \frac{1}{\sqrt{1-x^2}}=\frac{dt}{dx}\Rightarrow dx=\sqrt{1-x^2}dt\therefore I=\int \frac{t}{\sqrt{1-x^2}}\sqrt{1-x^2}dt=\int tdt=\frac{t^2}{2}+C=\frac{(si{n}^{-1}x{)}^2}{2}+C$