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Exp. integral

  1. Aug 21, 2006 #1
    hello

    could someone give me a pointer here.

    this integral
    ∫ln(x + c)dx

    my guess is, by integration by parts
    (ab)' = a'b + ab'
    ∫ba = ab - ∫b'a

    so here
    a = ln(c + x) b = c + x
    a' = 1/(c + x) b' = 1

    ab = (c + x)*ln(c + x)
    and
    ∫b'a = ∫ ((c + x)/(hc + x)) dx
    = ∫dx = x
    so ab - ∫b'a = (c + x)*ln(c + x) - x


    would this be correct?
     
  2. jcsd
  3. Aug 21, 2006 #2

    quasar987

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    I think you messed up a little bit in your re-writting the problem, but the answer (c + x)*ln(c + x) - x is correct. When it comes to integrals, you can always verify your answer by differentiating your answer. If it gives the integrand, you've got the right answer. If not, there's a mistake.
     
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