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

1. Jul 23, 2011

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?

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• substituion.png
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2. Jul 23, 2011

LCKurtz

If u = cos(x) then du = -sin(x)dx. It's in the du.

3. Jul 23, 2011

I suspected that but I then I got upset because I didn't know where the -ve went?

4. Jul 24, 2011

Ray Vickson

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

RGV

5. Jul 27, 2011