- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
Thanks to those who participated in last week's POTW!! Here's this week's problem!
-----
Problem: Let $J_n=\displaystyle\int\frac{\,dx}{(x^2+1)^n}$. Use integration by parts to prove that
\[J_{n+1} = \left(1-\frac{1}{2n}\right)J_n+\left(\frac{1}{2n}\right) \frac{x}{(x^2+1)^n}.\]
-----
Remember to read the POTW submission guidelines to find out how to submit your answers!
-----
Problem: Let $J_n=\displaystyle\int\frac{\,dx}{(x^2+1)^n}$. Use integration by parts to prove that
\[J_{n+1} = \left(1-\frac{1}{2n}\right)J_n+\left(\frac{1}{2n}\right) \frac{x}{(x^2+1)^n}.\]
-----
Remember to read the POTW submission guidelines to find out how to submit your answers!