How do I integrate (e^3lnx + e^3x)dx without a calculator?

[boardinchic]

Homework Statement

I have to integrate (e^3lnx + e^3x)dx

Homework Equations

The Attempt at a Solution

I have the answer and its (1/4)x^4 + (e^3x)/3 + C.
I don't know how to get to the answer without the help of my calculator.

 

[JasonRox]

I don't know how to get to the answer without the help of my calculator.

I'm not surprised.

 

[christianjb]

Do you mean e^[3ln(x)]?

Try and simplify that. Remember ln(y) is the inverse operation to e^y

 

[JasonRox]

I have to integrate (e^3lnx + e^3x)dx

So, is this e^3*lnx or e^(3*lnx)?

First, you can separate them into two integrals of e^(3*lnx) and e^3x. I assume you can solve the second one.

So, for the integral of e^(3*lnx), I'll give you a hint.

3*lnx = ln(x^3)

 

[boardinchic]

Thank you. I got that the e^lnx = x, but didn't know what to do with the 3. I get it now.