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Integrate the function
$\frac{1}{\sqrt{9-25 x^2}}$
$\frac{1}{\sqrt{9-25 x^2}}$
Solution:
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Verified Answer
$\int \frac{d x}{\sqrt{9-25 x^2}}=\frac{1}{5} \int \frac{d x}{\sqrt{\left(\frac{3}{5}\right)^2-x^2}}$
$=\frac{1}{5} \sin ^{-1}\left(\frac{x}{3 / 5}\right)+\mathrm{C}=\frac{1}{5} \sin ^{-1}\left(\frac{5 x}{3}\right)+\mathrm{C}$
$=\frac{1}{5} \sin ^{-1}\left(\frac{x}{3 / 5}\right)+\mathrm{C}=\frac{1}{5} \sin ^{-1}\left(\frac{5 x}{3}\right)+\mathrm{C}$
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