[tex]\int \frac{x-\tan^{-1} x}{x^3}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

I know the series form of tan-1 x = [tex] \sum_{n=0}^{\infty} \frac{x^{2n+1}}{2n+1} [/tex]

I know I need to subtract the x from that series and divide the x cubed form that series but i can't seem to be able to right the resulting series in a general form, any hints?

I thought it would be: [tex] -1/3x + \sum_{n=2}^{\infty} -x^{2n+2}/(2n+1)(2n+2)[/tex]. But this isnt it. Any Help?

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# Integral using series

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