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How to integrate Sin(x)e^Cos(x) using substitution.

  1. May 10, 2012 #1
    So a question for a test I just had was integrate by substitution:

    Sin(x)e^Cos(x).

    I did something like this:

    Let u=Cos(x)

    du=-sin(x) dx

    ∫sin(x)e^Cos(x) dx = ∫-e^u du

    =∫-e^Cos(x) du

    = -e ^cos (x) + c

    Is that correct??

    Thank you.





    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 10, 2012 #2

    It's correct but this step is weird. You calculate the integral with respect to u, then substitute back AFTER you've integrated.
     
  4. May 10, 2012 #3
    Thanks Clamtrox!!!

    So I meant to write:
    ∫sin(x)e^Cos(x) dx = ∫-e^u du
    =-e^u +c
    =-e^cos(x) +c
     
  5. May 10, 2012 #4

    SammyS

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    Hello donaldduck. Welcome to PF !

    That result looks good.

    Check the answer by finding the derivative of the result .
     
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