Solution: $\mathrm{I}=\int \frac{x^{7}}{\left(a^{2}-x^{2}\right)^{5}} d x$ Suppose $\mathrm{x}=a \sin \theta$ On differentiating both the sides we obtain $d x=a \cos \theta d \theta$...
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Exercise 19.13
Solution: Given that $\int \frac{x^{2}}{\left(a^{2}-x^{2}\right)^{3 / 2}} d x$ Putting $x=a \sin \theta$, then $d x=a \cos \theta d \theta$ and $\theta=\sin ^{-1}(x / a)$ The above equation becomes,...