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Integral help needed

  1. Jan 21, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\int \frac{26 dx}{{(169x^2+1)}^2}[/tex] <= the whole denominator is supposed to be squared...

    3. The attempt at a solution
    So I converted the thing in the denominator so that it has a square root:
    [tex]\int \frac{26 dx}{{\sqrt{169x^2+1}}^4}[/tex]

    Looking at the denominator, I realized I should do an inverse substitution:

    I subbed that in to the equation before and got:
    [tex]\int \frac{26 * sec^2(t) * dt}{13*sec^4(t)}[/tex]

    Simplifying which, I get:
    2[tex]\int cos^2(t) dt[/tex]

    Then I tried doing integration by parts, but I got nowhere - I kept getting cos^2 again... Please help me, this question frustrates me. Thanks in advance!

    (Sidenote: I finally got my formulas all pretty, yay!)
  2. jcsd
  3. Jan 22, 2009 #2


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    Science Advisor
    Homework Helper

    There's not really much profit into converting x^2 into sqrt(x)^4, is there? The rest of the general approach looks fine. You get sec^2/sec^4. So sure, cos^2(x). You just want to use a double angle formula cos(x)^2=(1+cos(2x))/2.
  4. Jan 22, 2009 #3
    Thanks! I know there isn't a point with the root, I'm just more used to seeing it like that. And thanks for the double angle formula. I always forget they exist... I guess it's time I memorize them :)
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