(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find

[tex]\int ln x^{2009}[/tex]

2. Relevant equations

The integration by parts!

3. The attempt at a solution

I have been trying to discover a series which might have helped:

I have taken out the integrals of :

1) ln x = x ln x -x

2) [tex]ln x^{2}[/tex]=x ([tex]ln x^{2}[/tex])-2x ln x +2x

3)[tex]ln x^{3}[/tex]=x[tex]ln x^{3}[/tex]-3x[tex]ln x^{2}[/tex]+6x ln x-6x

4)[tex]ln x^{4}[/tex]=x[tex]ln x^{4}[/tex]-4x[tex]ln x^{3}[/tex]+12x [tex]ln x^{2}[/tex]-12x ln x +12x

But I am unable to find a series. Please help!!

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# Homework Help: Integration of powers of ln x

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