# Math Help - Integration help

1. ## Integration help

Integral of ln(x)/x^2

2. Originally Posted by Link88
Integral of ln(x)/x^2
Try parts with $u=\ln(x)$...to make this a tad clearer try the sub $z=\ln(x)$ first

3. I had to do it twice and my final result was lnx

4. Originally Posted by Link88
I had to do it twice and my final result was lnx
If we do as I said and let $\ln(x)\longmapsto z$ then

\begin{aligned}\int\frac{\ln(x)}{dx}&\overbrace{\l ongmapsto}^{\ln(x)=z}\int\frac{z}{e^{2z}}\cdot e^z dz\\
&=\int z\cdot e^{-z}dz\\
&=-z\cdot e^{-z}-e^{-z}\quad{\color{red}\star}\\
&=\frac{-\ln(x)}{x}-\frac{1}{x}+C\end{aligned}

$\color{red}\star$ was gotten using integration by parts with $u=z$

5. Originally Posted by Link88
I had to do it twice and my final result was lnx
It always helps if you show your work ....