# Math Help - Integral of rational functions

1. ## Integral of rational functions

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

$
\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?

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

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

Factorise the denominator of the second term using the usual difference of two cubes formula and then break it up into partial fractions.