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Math Integration Solution 1. Find the integral $\int \frac{1}{\sqrt{a^2-x^2}} \, dx$ with respect to $x$ and hence evaluate $\int \frac{1}{\sqrt{9-25x^2}} \, dx$. Solution: Let $I = \int \frac{1}{\sqrt{a^2-x^2}} \, dx$ Substitute $x = a \sin\theta$, which means $\theta = \sin^{-1}\left(\frac{x}{a}\right)$ Differentiating both sides gives: $dx = a \cos\theta \, d\theta$ Substituting these into the integral: $$ \begin{align*} I &=.....

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