# Math Help - U substitution problem

1. ## U substitution problem

I am so lost right now.

the question is

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

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.

With your substitution, we have

\begin{aligned}
u&=1-4\ln x\\
du&=-\frac{4}{x}\,dx.
\end{aligned}

Our integral becomes

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