1. ## U substitution problem

I am so lost right now.

the question is

Integrate:$\displaystyle \frac{1}{x(1-4\ln x)^{-7}} dx$

I brought the 1 down and subsituted for (1- 4 lnx) but i cant work the derivative of u have a leftover of x dx to satisfy the problem. did i pick the wrong terms?

2. You are on the right track.

\displaystyle \begin{aligned} u&=1-4\ln x\\ du&=-\frac{4}{x}\,dx. \end{aligned}
$\displaystyle \int \frac{1}{xu^{-7}}\,dx=\int\left(-\frac{1}{4}\right)\cdot\left(-\frac{4}{x}\right)\cdot\frac{1}{u^{-7}}\,dx=-\frac{1}{4}\int u^7\,du.$