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Integrate (e^3lnx + e^3x)dx

  • #1

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.
 

Answers and Replies

  • #2
JasonRox
Homework Helper
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3
I don't know how to get to the answer without the help of my calculator.
I'm not surprised.
 
  • #3
529
1
Do you mean e^[3ln(x)]?

Try and simplify that. Remember ln(y) is the inverse operation to e^y
 
  • #4
JasonRox
Homework Helper
Gold Member
2,314
3
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)
 
  • #5
Thank you. I got that the e^lnx = x, but didn't know what to do with the 3. I get it now.
 

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