1. Integral of rational functions

I have no idea what direction to go in with this integral if anyone can please:

$\displaystyle \int_{}^{t} {t^3+a^3 \over t^3-a^3}dt$

I have made an attempt at polynomial long division but I dont think that is the way.
Not sure if using partial fraction decomposition is the way to go here?

$\displaystyle \int_{}^{t} {t^3+a^3 \over t^3-a^3}dt$
The integrand can be written as $\displaystyle 1 + \frac{2a^3}{t^3 - a^3}$.