Answer
$\displaystyle \frac{1}{5}\cdot\ln|5x-1|+C$
Work Step by Step
$\displaystyle \int\frac{1}{5x-1}dx=\int(5x-1)^{-1}dx$
Shortcut formula:
$\displaystyle \qquad\int(ax+b)^{-1}dx=\frac{1}{a}\ln|ax+b|+C$
With $ \left[\begin{array}{l}
a=5\\
b=-1
\end{array}\right],$
= $\displaystyle \frac{1}{5}\cdot\ln|5x-1|+C$
