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What type of integration to use?

  1. Feb 22, 2014 #1
    1. The problem statement, all variables and given/known data
    ∫(x2+9x)/(4x2) dx

    2. Relevant equations

    3. The attempt at a solution
    I started by using trigonometric substitution:
    dx=3sec2θ dθ

    ∫9(sec2θ)/4(9tan2)*3sec2θ dθ

    (3/4)∫(sec4θ)/(tan2θ) dθ

    I'm not really sure what to do next, or if I even used the best method of integration. Could I maybe use u substitution and let tanθ=u? Or maybe rewrite the integral as (1/cos4θ)/(sin2θ/cos2θ)
    Please help! Also if you have any tips on how to spot which integration techniques to use that would be great!
  2. jcsd
  3. Feb 22, 2014 #2


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    Gold Member

    you might try some algebraic manipulation before you even try a trig sub...
  4. Feb 22, 2014 #3
    Ohhh! I can't believe I overlooked that, thanks!
  5. Feb 22, 2014 #4


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    Homework Helper

    The sum is in the numerator, not the denominator, so the correct approach is to simplify.
  6. Feb 22, 2014 #5
    So now I have (1/4)∫(x+9)/(x) dx

    u substitution doesn't work, I don't know what to do next.
  7. Feb 22, 2014 #6


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    Gold Member

    You still haven't quite taken mine and pasmith's advice yet. It turns out no substitution is necessary.
  8. Feb 22, 2014 #7
    Oh, maybe I didn't understand what you meant then. I thought you just meant to cancel out the x's?
  9. Feb 22, 2014 #8

    D H

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    Staff Emeritus
    Science Advisor

    Write it as a sum of two integrals.
  10. Feb 22, 2014 #9
    Oh! Thanks so much, I forgot you could split up the numerator!
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