Question

$\int \frac{1}{\sqrt{9-25x^2}}dx$

Answer 1

$\int \frac{dx}{\sqrt{9-25x^2}}=\int \frac{dx}{5\sqrt{\frac{9}{25}-x^2}}$

$=\frac{1}{5}\int \frac{dx}{\sqrt{(\frac{3}{5}{)}^2-x^2}}$ $(\because \int \frac{dx}{\sqrt{a^{2-x^2}}}=si{n}^{-1}(\frac{x}{a})+c)$

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