Integrate the function 1 9-25 x^ 2 - Vidyadip

Question

Integrate the function $\frac{1}{\sqrt{9-25 x^{2}}}$

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Answer

Let 5x = t
$\Rightarrow$ 5dx = dt
$\Rightarrow \int \frac{1}{\sqrt{9-25 x^{2}}} d x= \frac15\int \frac{d t}{\sqrt{3^{2}-t^{2}}}$
$\Rightarrow \frac{1}{5} \sin ^{-1}\left(\frac{t}{3}\right)+C$
$\Rightarrow \frac{1}{5} \sin ^{-1}\left(\frac{5 x}{3}\right)+C$

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