# How do you integrate 1/(xlnx)dx?

Feb 15, 2015

Hello !

I propose another solution.

Remember that $\left(\setminus \ln \left(u\right)\right) ' = \setminus \frac{u '}{u}$ if $u$ is a positive differentiable function.

Take $u \left(x\right) = \setminus \ln \left(x\right)$ for $x > 1$ : it's a positive differentiable function.

Remark that $\setminus \frac{u ' \left(x\right)}{u \left(x\right)} = \setminus \frac{\setminus \frac{1}{x}}{\setminus \ln \left(x\right)} = \setminus \frac{1}{x \setminus \ln \left(x\right)}$, then

$\setminus \int \setminus \frac{\setminus \textrm{d} x}{x \setminus \ln \left(x\right)} = \setminus \ln \left(u \left(x\right)\right) + c = \setminus \ln \left(\setminus \ln \left(x\right)\right) + c$,

where $c$ is a real constant.