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Homework Help: Integral with e^x need help

  1. Sep 4, 2014 #1
    The problem I have is


    I cannot seem to get to the correct result, ln(e^2x + 1). I always have (e^2x)ln(e^2x + 1). What do I need to do, to get rid of the e^2x.
    Any help would be greatly appreciated.
  2. jcsd
  3. Sep 4, 2014 #2


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    Do the problem correctly. How's that for a nice vague reply? Unfortunately, that's about all anyone can say without seeing your work. How are we supposed to see where you're going wrong if you don't show your work?
  4. Sep 4, 2014 #3


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    Step 1. Try to simplify the problem (i.e., take any constants out of the integral).

    Step 2. You may want to try u-substitution.
  5. Sep 4, 2014 #4
    Hint: What's the derivative of e^2x?

    I think this is probably where the mistake was made.
  6. Sep 6, 2014 #5
    Its simple. Multiply your numerator and denominator by e^x. This will get you (2e^2x)/(e^2x + 1)dx. Now suppose your whole denominator as another variable,say, t. Calculate dt which will be equal to 2e^2xdx.
    So now your integral is in the form of (1/t)dt. Integration of this will give you ln(t). Substitute back the value of 't' and there you have it.
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