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Homework Help: U-substitution integral help

  1. Feb 28, 2010 #1
    determine the indef. integral:
    S= integral for me

    S 6/ (sqrt(x)*(x+81)) dx the (x+81) is not included within the sqrt

    I am stuck. I dont think U-substitution will work and im not sure about intigration by parts. It doens't look like i can use trig substitution either. Would partial fractions work? any suggestions please
     
  2. jcsd
  3. Feb 28, 2010 #2
    Re: Integral

    Try u^2 = x.
     
  4. Feb 28, 2010 #3
    Re: Integral

    so my du would be 1/2 x ^-1.2 ?
     
  5. Feb 28, 2010 #4
    Re: Integral

    Yup.
     
  6. Feb 28, 2010 #5
    Re: Integral

    alright thanks, ill work it out and see what i come up with
     
  7. Feb 28, 2010 #6
    Re: Integral

    ok heres what i got:

    = 6 S du/(u^2+81)... which is arc tan So

    = 6* 1/9 arctan (u/9) +C
    did i do the arctan right?
     
  8. Feb 28, 2010 #7
    Re: Integral

    Don't forget to swap back to x, though. Otherwise, great.
     
  9. Feb 28, 2010 #8
    Re: Integral

    oh yes, thanks!
     
  10. Feb 28, 2010 #9
    Re: Integral

    so its 6 * 1/9 arctan (sqrt (x) /9) +c
     
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