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Simple integration problem:help!

  1. Oct 27, 2013 #1
    Hi everyone,

    I just started to study Physics and I have a very simple question about integration. I'm blocked on this for a while. I'm trying to solve a differential equation for which I need to integrate the expression:
    ∫(e^2lnx)(10x)dx

    Does someone can tell me how to do it? I can't find this exact expression in formulas, and I've tried substitution with u = e^2lnx or with u = 2lnx and I've also tried to use ∫u'v = uv - ∫ uv' ... doesn't seem to work. Any idea?

    Thanks a lot!
     
  2. jcsd
  3. Oct 27, 2013 #2

    arildno

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    Eeh, are talking about:
    [tex]e^{2\ln(x)}[/tex]
    In that case, use the fact that ln(x) is the inverse function of e^x
     
  4. Oct 27, 2013 #3
    Thank you, so e^2ln(x) = 2x?? I know the rule e^lna = a but here it is e^blna that makes me confused. Is the rule here e^(bln(a)) = ba?
     
  5. Oct 27, 2013 #4

    arildno

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    Think about the following:

    How can you rewrite, by rules for exponentiation for real numbers:
    [tex](a^{b})^{c}=??[/tex]
     
  6. Oct 27, 2013 #5
    a^bc of course
     
  7. Oct 27, 2013 #6

    arildno

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    Of course!
    :smile:

    So, if you have e^(2*ln(x)), can you utilize the above identity in a clever way to simplify your expression, say by starting with: e^(2*ln(x))=e^(ln(x)*2)
     
  8. Oct 27, 2013 #7
    so here, it would be (e^2)(e^lnx) = x(e^2), you mean I should just see e^2 as a constant and taking it out of the integration?
     
  9. Oct 27, 2013 #8

    arildno

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    Eeh, no.
    Think again.
     
  10. Oct 27, 2013 #9
    Would it be (e^2)(e^lnx) = x^2??? It doesn't seem right...
     
  11. Oct 27, 2013 #10
    it would mean that e^blna = a^b
     
  12. Oct 27, 2013 #11

    arildno

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    Yup!
    :smile:
     
  13. Oct 27, 2013 #12

    arildno

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    Would it be (e^2)(e^lnx) = x^2??? It doesn't seem right.
    Your LHS is wrong, due to a faulty application of the rule.

    e^(2*ln(x))=x^2
     
  14. Oct 27, 2013 #13
    Phewww! Thanks!!:-):-)
     
  15. Oct 27, 2013 #14

    arildno

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    You're welcome!
    :smile:
     
  16. Oct 27, 2013 #15
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