# How do you integrate int 1/(x(lnx)^3) by parts?

Dec 1, 2016

If I had a choice, I would not use parts, I would use the substitution $u = {\left(\ln x\right)}^{-} 3$

#### Explanation:

If I was told I needed to use parts, I would take $u = 1$ so $\mathrm{du} = 0 \mathrm{dx}$ and $\mathrm{dv} = {\left(\ln x\right)}^{-} 3 \frac{1}{x} \mathrm{dx}$ so $v = - \frac{1}{2} {\left(\ln x\right)}^{-} 2$ (by sustitution).

$u v - \int v \mathrm{du} = - \frac{1}{2 {\left(\ln x\right)}^{2}} - \int 0 \mathrm{dx}$

$= - \frac{1}{2 {\left(\ln x\right)}^{2}} + C$

(I know it isn't " really" integration by parts.)