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Integration by parts

  1. Aug 29, 2004 #1
    hi, i would like help on a problem i am currently stuck on.

    [tex]\int(e^x)/(1+e^(2x))dx[/tex] <-- it's suppose to be [tex]\int[/tex] (e^x)/(1+e^(2x))dx

    using integration by parts, here's what i done:

    u=e^x
    du=e^x

    dv=(1+e^(2x))
    v = (need to use anti-differentiation, which i dont remeber....)

    can i use integration by parts with this? this is cal 2.
     
    Last edited: Aug 29, 2004
  2. jcsd
  3. Aug 29, 2004 #2
    Yes, v would be the integral of (1+e^(2x))
     
  4. Aug 29, 2004 #3

    Zurtex

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    Erm, by-parts doesn't seem to make sense because actually:

    [tex]u = e^x[/tex]

    [tex]dv = \frac{1}{1 + e^{2x}}[/tex]

    To me, it just looks like it is going to get nastier and nastier.

    I would suggest using the substitution [itex]t = e^x[/itex] because [itex]dt = e^xdx[/itex] and if you look at the integral like this it becomes quite simple:

    [tex]\int \frac{e^x dx}{1 + \left( e^x \right)^2} [/tex]
     
    Last edited: Aug 29, 2004
  5. Aug 30, 2004 #4

    nrqed

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    Hi,

    I would not try an integration by parts. I would simply do a simple substitution u= e^x. Then you have the integral of du/(1+u^2) which is a basic one.

    Pat
     
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