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

[adamwitt]

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.

 

[LCKurtz]

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

 

[adamwitt]

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

 

[Ray Vickson]

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

RGV

 

[adamwitt]

arghh hate that. cheers guy, appreciated.