How would I integrate exp(x)*cos(x)

[ComFlu945]

Homework Statement

How would I integrate exp(x)*cos(x), exp is referring to euler's number

Homework Equations

The Attempt at a Solution

u substitution doesn't work

 

[tiny-tim]

Hi ComFlu945!

Integrate by parts twice, and then use a bit of ingenuity.

 

[Hurkyl]

What would you even substitute? Well, I guess there are two or three things to try -- and you saw none of them worked out.

What other methods do you know?

 

[benorin]

$$e^x \cos x =\Re \, e^{(1+i)x}$$ which integrates nicely.

 

[Char. Limit]

Isn't that a bit complex (pun?) though?

I'd just do the integration by parts thing.

 

[tiny-tim]

$$e^x \cos x =\Re \, e^{(1+i)x}$$ which integrates nicely.

Yes, it's a nice trick, and it integrates nicely, but then you've got to simplify it, which is awkward and easy to get wrong.

 

[Hurkyl]

Not to mention it let's you avoid this wonderful exercise that reminds us of something that is often forgotten...