Question

Find the integral
1) $\int \frac{dx}{\sqrt{9-25x^2}}$

Answer 1

Sol :- $\int \frac{dx}{\sqrt{9-25x^2}}=\frac{1}{5}\int \frac{1}{\sqrt{\left(\frac{3}{5}\right)-x^2}}$

Using $\int \frac{1}{\sqrt{a^2-x^2}}=si{n}^{-1}\frac{x}{a}+c$

$=I=\frac{1}{5}\int \frac{1}{\sqrt{{\left(\frac{3}{5}\right)}^2-x^2}}=\frac{1}{5}si{n}^{-1}\frac{5x}{3}+c$