Math CentralQuandaries & Queries


Question from Slavena, a student:

integration of (lnx)^2 / x dx

Hi Slavena,

The integrand is

$$\frac{(\ln x)^2}{x} = \frac{1}{x} (\ln x)^2 .$$

What I see in this expression is the function $\ln x$ and the function $\large \frac{1}{x}.$ These are the functions that "pop out" at me since the derivative of $\ln x$ is $\large \frac{1}{x}.$ I immediately think that a substitution should help in evaluating this integral.

Try it and write back if you need more help,

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