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