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Integrating exponential functions

  1. Feb 18, 2010 #1
    How would you integrate something like xe(x^2) by using a substitution like u=x^2
     
  2. jcsd
  3. Feb 18, 2010 #2

    CompuChip

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    What is du?
     
  4. Feb 18, 2010 #3
    2x, but my problem is how will this help when you still have e raised to the power u
     
  5. Feb 18, 2010 #4
    Do you know what's

    [tex]\int e^{u}du[/tex]

    ?
     
  6. Feb 18, 2010 #5
    no this is what im stuck on
     
  7. Feb 18, 2010 #6
    Well, you know that integration is some sort of anti-derivative, and you know that a function of which derivative is e^x, is e^x it self. So it's safe to say that:

    [tex]\int e^{u}du=e^{u}+C[/tex]
     
  8. Feb 18, 2010 #7
    Thanks for your help, that cleared things up.
     
  9. Feb 18, 2010 #8
    just to clarify, du is 2x(dx), not just not 2x. i'm sure you already knew that though.
     
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