[tex]\int_{1} ^{2e} x^2(ln x)^{2} dx[/tex](adsbygoogle = window.adsbygoogle || []).push({});

I need to solve this using IbP. I made the following:

[tex]u = (ln x)^2[/tex]

[tex]du = (\frac{2 ln x}{x}) dx[/tex]

[tex]dv = x^2 dx[/tex]

[tex]v = \frac{x^3}{3}[/tex]

So I get:

[tex](ln x)^2 (\frac{x^3}{3}) \|_{1} ^{2e}[/tex][tex]- \int_{1} ^{2e} (\frac{x^3}{3}) 2 ln x dx[/tex]

(not sure how to make this look right)

Is this right?

Where do I go from here? Thanks

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# Intergration by Parts (IbP) problem

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