# Somewhat hard integral

1. Apr 30, 2012

### iRaid

1. The problem statement, all variables and given/known data
$$\int e^{3lnx} + e^{3x} dx$$

2. Relevant equations

3. The attempt at a solution

Not sure if I should use an e substitution or if I'm forgetting some easy e rules... Any help appreciated.

2. Apr 30, 2012

### Dick

You really have two separate problems there. e^(ln(x))=x will help with one of them.

3. Apr 30, 2012

### iRaid

e^(lnx)=x, do you mean the derivative of e^lnx=x? Why do they give me some stupid rule I don't know -.-"

4. Apr 30, 2012

### Dick

No, I mean e^(ln(x))=x. e^x and ln(x) are inverse functions. You didn't know that? Use that to simplify e^(3*ln(x)).

5. Apr 30, 2012

### iRaid

It's just too much to remember. Thank you though.

6. Apr 30, 2012

### Dick

You're welcome. It is pretty basic though. It's sort of the definition of what 'ln(x)' means.

7. Apr 30, 2012

### iRaid

Yeah I should of thought more, but I kind of instantly thought it was harder than I thought, usually what I do when I see e lol. Plus kind of stressed for this stupid AP exam -.-

8. Apr 30, 2012

### Dick

Well, try and destress. That's ones not that hard if you don't panic.

9. Apr 30, 2012

### iRaid

I know I know :\

10. Apr 30, 2012

### Dick

Good luck!

11. Apr 30, 2012

Thank you..