I've been dealing with several integrals involving rational functions. I have encountered myself arriving to an integral that requires the application of the following recursive formula:(adsbygoogle = window.adsbygoogle || []).push({});

[itex] \int\frac{1}{(u^2+α^ 2)^m} \, du= \frac{u}{2 α^ 2 (m-1)(u^2+α^ 2)^{m-1}}+\frac{2m-3}{2 α^2 (m-1)}\int\frac{1}{(u^2+α^ 2)^{m-1}} \, du [/itex]

as stated in Apostol'sCalculus.

However, I am curious about the demonstration of this formula. Apostol states in his book that it is obtained by integrating by parts, but I don't see how... does anybody have any ideas?

Thanks!

Bibliography

Calculus, Volume 1, One-variable calculus, with an introduction to linear algebra, (1967) Wiley, ISBN 0-536-00005-0, ISBN 978-0-471-00005-1

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# How to obtain the rational function integration recursive formula

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