- #1
Chris L T521
Gold Member
MHB
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Thanks to those who participated in last week's POTW! Here's this week's problem!
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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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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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