Homework Help: Integral of e^x(cosx)?

1. Dec 19, 2011

theBEAST

1. The problem statement, all variables and given/known data
I attached a picture of my attempt, it seems to loop back... Maybe I made a mistake... If not how am I suppose to integrate this? Thank you!

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2. Dec 19, 2011

Dick

Stop at the third line. Now move the integral of cos(x)*e^x on the right to the left. Then you are basically done. The third line gives you an equation where the only integral is cos(x)*e^x. Solve for it.

3. Dec 19, 2011

theBEAST

Oh I see, I got

∫(e^xcosx dx)=(e^xsinx+e^xcosx)/2

But how did I get :
∫(e^xcosx dx)=e^xsinx+e^xcosx-∫(e^xcosx dx) (in the third step)

and

∫(e^xcosx dx)=∫(e^xcosx dx) (in the last step)

The two are not the same thing?

4. Dec 19, 2011

Dick

Both of those statements are true. The first one tells you something useful. The second one is also true. But it doesn't tell you anything useful. They don't conflict with each other.

Last edited: Dec 19, 2011
5. Dec 20, 2011

cragar

there is a really slick way to do this with Eulers formula. using e^(ix)=isin(x)+cos(x)
By substituting e^(ix) in and then taking the real part at the end.