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

1. Jan 21, 2010

### ComFlu945

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

u substitution doesn't work

2. Jan 21, 2010

### tiny-tim

Hi ComFlu945!

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

3. Jan 21, 2010

### Hurkyl

Staff Emeritus
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?

4. Jan 21, 2010

### benorin

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

5. Jan 21, 2010

### Char. Limit

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

I'd just do the integration by parts thing.

6. Jan 21, 2010

### tiny-tim

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.

7. Jan 21, 2010

### Hurkyl

Staff Emeritus
Not to mention it lets you avoid this wonderful exercise that reminds us of something that is often forgotten....