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

  1. Mar 18, 2007 #1
    1. The problem statement, all variables and given/known data
    I have to integrate (e^3lnx + e^3x)dx

    2. Relevant equations

    3. 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.
  2. jcsd
  3. Mar 18, 2007 #2


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    I'm not surprised.
  4. Mar 18, 2007 #3
    Do you mean e^[3ln(x)]?

    Try and simplify that. Remember ln(y) is the inverse operation to e^y
  5. Mar 18, 2007 #4


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    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)
  6. Mar 18, 2007 #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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