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- Jan 26, 2012

- 995

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**Problem**: Let $J_n=\displaystyle\int\frac{\,dx}{(x^2+1)^n}$. Use integration by parts to prove that

\[J_{n+1} = \left(1-\frac{1}{2n}\right)J_n+\left(\frac{1}{2n}\right) \frac{x}{(x^2+1)^n}.\]

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