The Purplemath Forums

by **yabo2k** on Thu May 07, 2009 1:03 am

find the antiderivative of (((ln(x))^2)/x dx. I am not sure how to go about solving this.

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by **Martingale** on Thu May 07, 2009 2:20 am

yabo2k wrote:find the antiderivative of (((ln(x))^2)/x dx. I am not sure how to go about solving this.

let $u=\ln(x)$

by **yabo2k** on Thu May 07, 2009 10:17 pm

so I get...(((ln(x))^2)+C

by **stapel_eliz** on Thu May 07, 2009 10:18 pm

If you're not sure, differentiate, and see if you end up with the original integrand. :wink:

by **Martingale** on Thu May 07, 2009 11:01 pm

yabo2k wrote:so I get...(((ln(x))^2)+C

not quite.

by **yabo2k** on Fri May 08, 2009 12:05 am

so my u=ln(x) and my du= (1/x)dx

so using u and du i get......du(u)^2

so is my answer ((ln(x)^3)/3)+C

by **Martingale** on Fri May 08, 2009 12:19 am

yabo2k wrote:so my u=ln(x) and my du= (1/x)dx

so using u and du i get......du(u)^2

so is my answer ((ln(x)^3)/3)+C

yes

find the antiderivatie of (((ln(x))^2)/x dx