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Anti-Derivative of e^x/2

  1. Jan 29, 2016 #1
    1. The problem statement, all variables and given/known data
    I am working on an integration by parts problem, and in order to work it I need to figure out the anti-derivative of ex/2. We've covered basic integration concepts, the definite/indefinite integral, u-sub, and integration by parts. Now, examining the derivative, I expect the anti-derivative to be 2ex/2, but I can't show my work on how I get here. I tried u-sub and I just get the same function.
     
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  3. Jan 29, 2016 #2

    BvU

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  4. Jan 29, 2016 #3

    blue_leaf77

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    I think the OP is not dealing with a Gaussian function.
     
  5. Jan 29, 2016 #4

    BvU

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    Oh boy, misread. And answered too quickly - again. Sorry.

    Dear Rye,

    if you differentiate ##e^{x\over 2}## you get ## {1\over 2}e^{x\over 2}## so the ##2e^{x\over 2}## you found is indeed a primitive of ##e^{x\over 2}##.

    You state you get the same function. Should n't be the case. If ##e^y## is a primitive of ##e^y## then the substitution ## y = {x\over 2}## and the chain rule give $$ {d \; e^y \over dx} = {d\; e^y \over dy} {dy\over dx} = {d \; e^y \over dy} \; {1\over 2} = {1\over 2} \; e^y \;$$

    (but maybe I have no idea what u-subbing is ...)
     
    Last edited: Jan 29, 2016
  6. Jan 29, 2016 #5

    Ray Vickson

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    What is your problem? You say you used u-substitution and got the same function, which is fine, since your answer is correct!
     
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