(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use integration by parts to derive the formula:

[tex]\int (a^2 - x^2)^n dx = \frac{x(a^2-x^2)^n}{2n+1} + \frac{2a^2n}{2n+1}\int \frac{(a^2 - x^2)^n}{(a^2 - x^2)} dx + C [/tex]

2. Relevant equations

Integration by parts general formula

∫udv = uv - ∫vdu

3. The attempt at a solution

I tried the following:

[tex] u = (a^2 - x^2)^n, dv = 1 [/tex]

This gave me another integral, as expected. However, further applications of integration by parts didn't give me the right answer. I am still looking for other terms for 'u' and 'dv'.

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# Integration by parts problem

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