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Math Help - Polynomial indefinite integral

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    Polynomial indefinite integral

    Hello, I'm in calculus 2 and have this problem:

    \int \frac{t^2-3}{-t^3+9t+1}dt

    Separating the numerator does not seem to do any good. How should I proceed?
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  2. #2
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    Re: Polynomial indefinite integral

    Quote Originally Posted by Ragnarok View Post
    Hello, I'm in calculus 2 and have this problem:

    \int \frac{t^2-3}{-t^3+9t+1}dt
    Note that \int \frac{t^2-3}{-t^3+9t+1}dt=\frac{-1}{3}\int \frac{-3t^2+9}{-t^3+9t+1}dt
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    Re: Polynomial indefinite integral

    Thanks! But I still don't get it. How does that help?
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    Re: Polynomial indefinite integral

    Okay, never mind, I got it. So the point here was that we needed to make the numerator something that would cancel out the derivative of the denominator?
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    Re: Polynomial indefinite integral

    Quote Originally Posted by Ragnarok View Post
    Okay, never mind, I got it. So the point here was that we needed to make the numerator something that would cancel out the derivative of the denominator?
    Yes. The moral of the story, always look for an "inner" function with its derivative as a multiple, then you can use a substitution.
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    Re: Polynomial indefinite integral

    Let u = -t^3 + 9t + 1. What is du/dx?
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