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Math Help - Integral [Calc 2]

  1. #1
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    Integral [Calc 2]

    There was a question on a previous exam and I can't seem to get the right answer.

    \int\frac{2dx}{x^3 + x}

    My initial method was to use Integration by Parts, but I can't seem to massage it correctly.

    u = \frac{2}{x}; du = 2ln(x)dx

    dv = (x^2 + 1) dx; v = \frac{x^3}{3} + x

    Fairly certain this doesn't work though, although my arithmetic could be off.
    Could someone please take a jab at this? I would appreciate it greatly. :]
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  2. #2
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    Quote Originally Posted by freyrkessenin View Post
    There was a question on a previous exam and I can't seem to get the right answer.

    \int\frac{2dx}{x^3 + x}

    My initial method was to use Integration by Parts, but I can't seem to massage it correctly.

    u = \frac{2}{x}; du = 2ln(x)dx

    dv = (x^2 + 1) dx; v = \frac{x^3}{3} + x

    Fairly certain this doesn't work though, although my arithmetic could be off.
    Could someone please take a jab at this? I would appreciate it greatly. :]
    Use a partial fraction decomposition.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Use a partial fraction decomposition.

    Ah. That's why I couldn't do it. I never learned how to do partial fractions. But thanks. :]
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  4. #4
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    Put x=\frac1u and you'll get an easy integral.
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