First excuse my bad english on math subjects. I'm working on it.(adsbygoogle = window.adsbygoogle || []).push({});

How can I integrate by parts:

[tex] I_{m}=\int\frac{1}{(x^2+a^2)^m}\,dx[/tex]

I need to find a recursive form,

But I can't find the right g' and f to get this done...

I've tried

[tex] g'=1 \quad\,\quad\ f=\frac{1}{(x^2+a^2)^m}[/tex]

As well as [tex]g' = \frac{1}{(x^2+a^2)}\quad\ →g=arctan(x/a)\ , \quad\ f=\frac{1}{(x^2+a^2)^{m-1}} [/tex]

But on the next integral of g*f ' , I can't find any way to simplify it to I_{m-1}or another integration by parts that will lead somewhere.

Which g' and f should I pick for this integral then? Thanks in advance..

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# Recursive integral using integration by pars

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