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Math Help - U substitution problem

  1. #1
    Junior Member
    Joined
    Dec 2009
    Posts
    46

    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?
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  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    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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