Question

Integrate the following functions.
$\int \frac{1}{\sqrt{9-25x^2}}dx$

Answer 1

$\int \frac{1}{\sqrt{9-25x^2}}dx=\int \frac{1}{\sqrt{25\left[\right(\frac{3}{2}{)}^2-x^2]}}dx=\frac{1}{5}\int \frac{1}{\sqrt{\left[\right(\frac{3}{5}{)}^2-x^2]}}dx=\frac{1}{5}si{n}^{-1}\left(\frac{x}{\frac{3}{5}}\right)+C[\because \int \frac{dx}{\sqrt{a^2-x^2}}=si{n}^{-1}(\frac{x}{a}\left)\right]$

$=\frac{1}{5}si{n}^{-1}\left(\frac{5x}{3}\right)+C$