What is the Integral of e to the Power of 3lnx and e to the Power of 3x?

[iRaid]

Homework Statement

\int e^{3lnx} + e^{3x} dx

Homework Equations

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.

 

[Dick]

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

 

[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 -.-"

 

[Dick]

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

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)).

 

[iRaid]

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

 

[Dick]

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

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

 

[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 -.-

 

[Dick]

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 -.-

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

 

[iRaid]

I know I know :\

 

[Dick]

I know I know :\

Good luck!

 

[iRaid]

Thank you..