Step 1:
First, we rewrite the integral by factoring out a 25 from under the square root:
$$
\int \frac{1}{\sqrt{9-25 x^{2}}} dx = \int \frac{1}{\sqrt{25( \frac{9}{25} - x^{2})}} dx = \frac{1}{5} \int \frac{1}{\sqrt{(\frac{3}{5})^{2} - x^{2}}} dx
$$
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