# Taking imaginary integral and derivative

1. Nov 17, 2012

### chaotic

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

when im solving quantum problem, i see an equation like e^(-kx) e^(icx) i is imaginary. how can i take the integral and derivative of this function

2. Relevant equations

e^ix ) cosx + isinx

3. The attempt at a solution

actually i tried e^x(-k+ic) and i said the derivative is just (-k+ic)* e^x(-k+ic) :)

2. Nov 17, 2012

### voko

What you did is correct. You can treat complex constants as if they were real in differentiation and integration. However, I would recommend getting some introductory text on complex analysis and study it at least until differentiation and integration are introduced.

3. Nov 17, 2012

### chaotic

4. Nov 17, 2012

### voko

That's because it is confused by the input. Note it treats "icx" as all caps CIX and assumes it is a constant.

5. Nov 17, 2012

### chaotic

agh :) thank you very much i understand now :)

6. Nov 17, 2012

### haruspex

Wolfram seems to have treated the second x as some constant X. In fact, it looks suspiciously as though it has interpreted "icx" as Roman Numerals "CIX" (109). Bizarre.

7. Nov 17, 2012

### chaotic

yes it is very confusing im trying to find solution for 2 hours just because of that it is funny it takes my precious time :)

8. Nov 17, 2012

### voko

A space after i and before c does wonders. But the output is still a bit odd.

9. Nov 17, 2012

### SammyS

Staff Emeritus
Yes, $\ \ i(c+i k) e^{-k x+i c x}\ \$ is a bit odd, isn't it?