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U substitution

  1. Feb 3, 2014 #1
    1. The problem statement, all variables and given/known data
    ∫(4x)/(x2+9) dx

    2. Relevant equations



    3. The attempt at a solution
    Originally I tried to solve with u substitution:

    u=x2+9
    du=2x dx
    1/2du=dx
    ∫2/u
    =2lnu+C
    =2ln(x2+9)+C

    But shouldn't arctan be somewhere in the answer?
     
  2. jcsd
  3. Feb 3, 2014 #2
    Oops, I made a typo.
    1/2xdu=dx
     
  4. Feb 3, 2014 #3

    SteamKing

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    What's the derivative of an arctan function?

    In any event, if you differentiate your answer, you should obtain the original integrand.
     
  5. Feb 3, 2014 #4
    Is it (1/1+x2)?
     
  6. Feb 3, 2014 #5

    Curious3141

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    Yes, assuming you meant ##\frac{1}{1+x^2}##, because your parentheses are placed wrongly. But ##\frac{x}{1+x^2}## is a completely different expression from ##\frac{1}{1+x^2}##. In this case, you have something more like the former. Hence no arctan in the integral.
     
  7. Feb 3, 2014 #6
    But I don't understand why u substitution doesn't work?
     
  8. Feb 3, 2014 #7

    Curious3141

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    Who said it doesn't work? Your integral in the first post is correct.
     
  9. Feb 3, 2014 #8
    Really?? When I went to a tutoring center at my university the tutor told me that I needed to use arctan? Or was she just saying that its another method of doing it?
     
  10. Feb 3, 2014 #9
    No. She was saying it because she was wrong.
     
  11. Feb 3, 2014 #10
    Hahaha! Thanks for your help everybody :)
     
  12. Feb 4, 2014 #11
    To be fair, it's possible that by "use arctan" the tutor meant to use a trig sub ##\tan\theta=x##, which would be the same as ##u=\arctan x##. This would work, though it'd most definitely be a more involved approach than the simple u-sub suggested in the thread.
     
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