
U substitution problem
I am so lost right now.
the question is
Integrate:$\displaystyle \frac{1}{x(14\ln x)^{7}} dx$
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?

You are on the right track.
With your substitution, we have
$\displaystyle \begin{aligned}
u&=14\ln x\\
du&=\frac{4}{x}\,dx.
\end{aligned}$
Our integral becomes
$\displaystyle \int \frac{1}{xu^{7}}\,dx=\int\left(\frac{1}{4}\right)\cdot\left(\frac{4}{x}\right)\cdot\frac{1}{u^{7}}\,dx=\frac{1}{4}\int u^7\,du.$