Question

Integrate the function $\frac{1}{\sqrt{9-25x^2}}$

Answer 1

Let $5x=t$
$\therefore 5dx=dt$
$\Rightarrow \int \frac{1}{\sqrt{9-25x^2}}dx=\frac{1}{5}\int \frac{1}{\sqrt{9-t^2}}dt$
$=\frac{1}{5}{\sin }^{-1}\left(\frac{t}{3}\right)+C$
$=\frac{1}{5}{\sin }^{-1}\left(\frac{5x}{3}\right)+C$