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Homework Help: Who can solve this integral?

  1. Aug 20, 2008 #1
    Can someone solve this integral as the answer, please? I'm sure it is easy for you:

    see attached picture, please! :)
     

    Attached Files:

  2. jcsd
  3. Aug 20, 2008 #2

    Defennder

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    What have you attempted? Use integration by parts.
     
  4. Aug 20, 2008 #3
    hi,

    integration by parts seems to be right!

    I just don't get through the first steps... help! ;)
     
  5. Aug 20, 2008 #4

    Defennder

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    What is formula for integration by parts? What should you let u and dv be?
     
  6. Aug 20, 2008 #5
    S u dv = uv - S v du

    u= ln(x+5)
    dv= (x^3)/3


    I just don't know how to solve it if where there is an addition after ln(...)

    thanks
     
  7. Aug 20, 2008 #6

    Defennder

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    dv isn't x^3/3, that's v.

    So you need to find du now. Or du/dx. Check out the derivative of function ln(f(x)). Then plug that into the formula.
     
  8. Aug 20, 2008 #7
    thanks
     
  9. Aug 20, 2008 #8
    hi, now I'm there

    ln(x+5) x^3/3 - 1/3 S x^3 1/(x+5) dx

    how can i solve this integral?

    S x^3 1/(x+5) dx


    thank you again!!!
     
  10. Aug 20, 2008 #9

    tiny-tim

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    Welcome to PF!

    Hi tommy_ita! Welcome to PF! :smile:

    (have an integral: ∫ and a cubed: ³)

    You mean ∫x³dx /(x + 5) …

    either long-division to get a constant/(x + 5) plus a quadratic,

    or substitute y = x + 5, integrate, and substitute back again. :smile:

    (in hindsight, making that substitution before integrating by parts might have been simpler :wink:)
     
  11. Aug 21, 2008 #10
    hi tiny-tim,

    thanks for the ∫ :D


    unfortunately, I am not able to find the solution. Could you help me by doing the integral step-by-step?
    that'd be very nice

    ∫x³dx /(x + 5) =
     
  12. Aug 21, 2008 #11

    tiny-tim

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    Hi tommy_ita! :smile:

    When in doubt. use the obvious substitution, in this case:

    y = x + 5, dy = dx,

    ∫x³dx /(x + 5) = ∫(y - 5)³dy /y = ∫(Ay² + By + C + (D/y))dy …

    and you can fill in the rest yourself, can't you? :smile:
     
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