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Thread: Quick Integration Problem

  1. May 25th 2011, 06:03 PM #1
    Status
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    Quick Integration Problem

    Hi,

    I'm doing review problems for an upcoming exam and I'm stuck on this problem.

    \int \frac {1}{x^2-6x+58}dx

    How should I proceed? I'm guessing I have to do something to the denominator first but I'm not sure what.

    Thanks for the help.
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  2. May 25th 2011, 06:05 PM #2
    TheEmptySet
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    Behold, the power of SARDINES!
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    Quote Originally Posted by Status View Post
    Hi,

    I'm doing review problems for an upcoming exam and I'm stuck on this problem.

    \int \frac {1}{x^2-6x+58}dx

    How should I proceed? I'm guessing I have to do something to the denominator but I'm not sure what.

    Thanks for the help.
    Since the denominator does not factor over the reals you need to complete the square.

    x^2-6x+58=(x^2-6x+9)+49=...
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  3. May 25th 2011, 06:08 PM #3
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    Ah I got it. Thank you!
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  4. May 25th 2011, 06:13 PM #4
    skeeter
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    Quote Originally Posted by Status View Post
    Hi,

    I'm doing review problems for an upcoming exam and I'm stuck on this problem.

    \int \frac {1}{x^2-6x+58}dx

    How should I proceed? I'm guessing I have to do something to the denominator first but I'm not sure what.

    Thanks for the help.
    note ...

    \int \frac{1}{x^2+a^2} \, dx = \frac{1}{a}\arctan\left(\frac{x}{a}\right) + C
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