U substitution problem

**x5pyd3rx** · February 24th 2010, 04:44 PM

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?

**Scott H** · February 24th 2010, 06:10 PM

You are on the right track.

With your substitution, we have

$\begin{aligned}<br /> u&=1-4\ln x\\<br /> du&=-\frac{4}{x}\,dx.<br /> \end{aligned}$

Our integral becomes

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

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