(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex] \int e^{2x}sin(e^x)dx [/tex]

2. Relevant equations

Can I make the substitution:

[tex] w = e^x ; dw = e^x dx [/tex]

Making a "new / simpler" problem:

[tex] \int w sin(w) [/tex]

3. The attempt at a solution

Using integration by parts on the "new" problem:

[tex] u = w ; dw = du [/tex]

[tex] dv = sin (w) ; v = -cos(w)[/tex]

[tex] \int w sin(w) dw = -w cos(w) +\int cos(w) dw [/tex]

[tex]= -w cos(w) + sin(w)[/tex]

[tex]= -e^xcos(e^x) + sin(e^x) [/tex]

is this correct?

This integral is part of a larger problem and this term should "go away" supposedly.

If this is correct (this solution does not simplify to 0), then I will need to post the larger problem -

Thanks for the help

-Sparky

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# Homework Help: Integration by parts

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