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Integration by Subtitution: sin(x).cos(x).(e^cos(x))

  1. Jul 23, 2011 #1
    Problem attached as image. Solution included.

    I am fine with getting the integrating factor, that bits the easy bit obviously.
    But Basically my specific problem is when I try to integrate sin(x).cos(x).(e^cos(x))

    I understand that I need to use substitution here, but I'm not sure how they have done it.
    Why does the sin(x) suddenly disappear? Where did it go during the substitution?

    Can someone please explain this for me? many thanks in advance.

    Attached Files:

  2. jcsd
  3. Jul 23, 2011 #2


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    If u = cos(x) then du = -sin(x)dx. It's in the du.
  4. Jul 23, 2011 #3
    I suspected that but I then I got upset because I didn't know where the -ve went?
  5. Jul 24, 2011 #4

    Ray Vickson

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    There seems to be a "typo" in the attached document.

  6. Jul 27, 2011 #5
    arghh hate that. cheers guy, appreciated.
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