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Math Help - Trig Substitution Integral

  1. #1
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    Trig Substitution Integral

    Need help with integrating: 1/((x^2-6x+11)^2)
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  2. #2
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    Jun 2008
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    \int \frac{1}{(x^2-6x+11)^2}dx

    First, complete the square in the denominator:
    \int \frac{1}{(x^2-6x+9+2)^2}dx=\int \frac{1}{((x-3)^2+2)^2}dx

    Take 2 common factor: \frac{1}{4} \int \frac{1}{((\frac{x-3}{\sqrt{2}})^2+1)^2}dx

    Now sub \frac{x-3}{\sqrt{2}} = \tan{\theta} and continue.
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