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Inverse Trig Integration - Can I use u-substitution?

  1. Jan 14, 2006 #1
    Here is the problem and the solution manual's solution to the problem. I couldn't see that I had to add 6 and subtract 6 in the numerator then split the integral into two separate integrals. Is there an easier way to do it using u-substitution? Are their alternative ways to evaluate this integral?

    [​IMG]

    Thanks
     
  2. jcsd
  3. Jan 15, 2006 #2

    siddharth

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    Homework Helper
    Gold Member

    From my experience, adding and subtracting 6 is the standard and easiest way to proceed.

    The clue to add and subtract 6 is that, you want to express the numerator as the complete derivative of the denominator.

    ie,
    [tex] \frac{d}{dx} (x^2 + 6x +13) = 2x + 6 [/tex]
    Which enables you to use the substitution [itex] x^2 + 6x +13 = u [/itex].

    The second part, ie, [tex] -6 \int \frac{1}{x^2 + 6x +13} dx [/tex] is then a standard integral.
     
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