homework and exercises - First integral of an equation of motion: $muddot r=-frac{k}{r^2}$

I've got an equation of motion (EOM), which is

$$ \mu\ddot r=-\frac{k}{r^2} $$

How do I find the first integral of this EOM? I'd appreciate it if someone could show me the steps involved. I should get

$$ \frac{1}{2}\mu\dot r^2=-k \left( \frac{1}{R}-\frac{1}{r} \right) $$

but I'm not sure how to proceed.