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Need some help with an integral.

  1. Oct 23, 2013 #1
    Hey! Need some help on an integral I've been trying to solve. I haven't been working enough with my math, so I am working on catching up before finals..

    I was working with partial fractions and u substitution when I couldn't figure this one out:

    ∫(x+5)/(x^2+4x+8)dx

    it's not that hard but I am missing one small detail in order to solve it, I am sure.

    I believe the answer has something to do with

    ∫1/(a^2+x^2)dx = 1/a arctan(x/a) + C

    Thanks
     
  2. jcsd
  3. Oct 23, 2013 #2

    arildno

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    Dearly Missed

    1. Complete the square in the denominator!
    2. In the numerator, write 5=2+3, and then see if an idea pops up in how to solve the problem!
    :smile:
     
  4. Oct 23, 2013 #3
    Sooo if I say:

    ∫(x+2+3)/((x+2)^2+4)dx and substitute x+2 with u, and dx with du

    ∫(u+3)/(u^2+4)du am I on the right track? I'll have it done in a minute and check the answer.

    thanks.

    ************EDIT****************

    lots of stuff happend and then:

    1/2 ln((x+2)^2+4) + 3/2 arctan((x+2)/2) ?
     
    Last edited: Oct 23, 2013
  5. Oct 23, 2013 #4

    Mark44

    Staff: Mentor

    You can check your antiderivative by differentiating it. If you end up with the original integrand, you're golden.
     
  6. Oct 24, 2013 #5

    arildno

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    The right stuff happened!
    :smile:
     
  7. Oct 24, 2013 #6
    Don't forget the arbitrary constant +C :devil:
     
  8. Oct 24, 2013 #7
    Don't worry, I didn't :) I just forgot to write it here :)
     
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