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Math Help - Integrate problem with partial fractions

  1. #1
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    Integrate problem with partial fractions

    Evaluate

     \int_{}^{t}dt\frac{t^3+a^3}{t^3-a^3}

    So far i have


     \int_{}^{t}dt\frac{t^3+a^3}{t^3-a^3} = \int_{}^{t}dt\frac{t^3-a^3+a^3+a^3}{t^3-a^3} = \int_{}^{t}dt\frac{t^3-a^3}{t^3-a^3}+\frac{2a^3}{t^3-a^3} = \int_{}^{t}dt1+\frac{2a^3}{t^3-a^3}

    I'm not sure where i am to go next. Any hints as to what i can do?
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  2. #2
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     \int 1 + \frac{2a^3}{x^3 - a^3} dt = t + 2a^3 \int \frac{dt}{x^3 - a^3}

    Use the "difference of cubes" formula and the denominator should factor to a product of a linear expression and an irreducible quadratic. Then you can use partial fractions.
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Karl Harder View Post
    Any hints as to what i can do?
    Factor...
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