Evaluate: `int(x^7)/((a^2-x^2)^5)dx`

Explanation

Let `1=int frac{x^{7}}{(a^{2}-x^{2})^{5}} d x`
`
Let x=a sin theta`

On differentiating both sides, we get
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d x=a cos theta d theta `
`
I=int frac{a^{8} sin ^{7} theta cos theta}{(a^{2}-a^{2} sin ^{2} theta)} `
`
=int frac{a^{8} sin ^{7} theta cos theta}{a^{10}(1-sin ^{2} theta)^{5}} d theta `
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