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Math Help - Integration via completing the square

  1. #1
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    Integration via completing the square

    When using completing the squares on a fraction do I alter both the numerator and denominator? ex... (x-1)/(x^2-4x+5) ???/(x-2)^2+1
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  2. #2
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    Like so:

    \int\frac{x-1}{(x-2)^{2}+1}

    Now, let u=x-2, \;\ du=dx, \;\ u+1=x-1

    \int\frac{u+1}{u^{2}+1}du=\int\frac{u}{u^{2}+1}+\i  nt\frac{1}{u^{2}+1}du

    Now, make the observation that there will be an ln and arctan in your future.
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