Answer
$\ln |4r^2-5|+c$
Work Step by Step
Solve $\int\dfrac{8rdr}{4r^2-5}$
Let $p=4r^2-5$ and $dp=8rdr$
This implies $\int\dfrac{8rdr}{4r^2-5}=\int\dfrac{dp}{p}=\ln|p|+c$
Since, $p=4r^2-5$
Thus, $\int\dfrac{8rdr}{4r^2-5}=\ln |4r^2-5|+c$