# integration by parts

by Rasine
Tags: integration, parts
 P: 214 intergrate (ln(x))^2 so i set u=(lnx)^2...which makes du=2lnx(1/x) then i set dv=dx...which makes v=x according to the formula for integration by parts i have x(lnx)^2- integral x(2lnx)(1/x) simplifying it i get x(ln)^2-2intergral lnx and here is where i am stuck....what i the integral of lnx?
 Mentor P: 8,287 The derivative of (lnx)^2=(2lnx)/x. [edit: of course that's you've written... i glanced and say ln(1/x)... sorry ] A hint for integrating lnx; use parts, taking dv=dx and u=lnx
 P: 2,048 How about integration-by-parts once again? :)
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## integration by parts

xln(x) - x looks good from where I'm standing.

I just wondered "what function gives ln(x) when differentiated? Well ln(x)' = 1/x. So what if I try xln(x)? Now I get ln(x) + 1. So I need to add something to the mix that gives -1 when differentiated." Hence xln(x) - x.
 P: 214 ohhh yes......do integration by part again........ thank you!

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