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Math Help - Integral of rational functions

  1. #1
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    Integral of rational functions

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

     <br />
\int_{}^{t} {t^3+a^3 \over t^3-a^3}dt<br />

    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?
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    Quote Originally Posted by shadow85 View Post
    I have no idea what direction to go in with this integral if anyone can please:

     <br />
\int_{}^{t} {t^3+a^3 \over t^3-a^3}dt<br />
    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.
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