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Indefinite integral problem

  1. Nov 10, 2012 #1
    1. The problem statement, all variables and given/known data
    F(x)= (3^x)(e^x)dx



    2. Relevant equations
    F(u)=U^n=(U^(n+1))/n+1


    3. The attempt at a solution
    I said it equaled:
    ((3^(x+1))/(x+1))(e^x)
     
  2. jcsd
  3. Nov 10, 2012 #2

    vela

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    Your post doesn't make sense. Why don't you write things out using normal notation so we don't have to guess as to what you mean?
     
  4. Nov 10, 2012 #3

    HallsofIvy

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    You've made a number of very basic errors. First, and this may be what Vela was complaining about, it doesn't make sense to have a function equal to an integrand- what you meant to say, instead of [itex]F(x)= 3^xe^xdx[/itex] was that the integrand was [itex]3^x e^x dx[/itex] or, equivalently that you were trying to find [itex]F(x)= \int 3^xe^x dx[/itex].

    You make the same kind of error when you write "F(u)=U^n=(U^(n+1))/n+1". [itex]U^{n+1}/(n+1)[/itex] is the integral of [itex]U^n[/itex], they are not equal. (Oh, and two minor things- "u" and "U" are not interchangeable and what you wrote, U^(n+1)/n+ 1 is equal to (U^(n+1)/n)+ 1, not U^(n+1)/(n+1).)

    Most importantly, that "power rule" does not apply here. It applies to the variable to a constant power and what you have here is a constant to a variable power. And, of course, you cannot simply multiply by [itex]e^x[/itex] as if it were a constant.

    Instead, use the fact that [itex]3^x= e^{ln 3^x}= e^{xln(3)}[/itex] and write the integral, [itex]\int 3^xe^x dx[/itex], as [itex]\int e^{x ln(3)}e^x dx= \int e^{x ln(3)+ x}dx= \int e^{x(ln(3)+ 1)}dx[/itex].

    Now, do you know how to integrate [itex]\int e^{ax}dx[/itex]?
     
  5. Nov 12, 2012 #4
    no i do not. can you tell me please?
     
  6. Nov 12, 2012 #5

    HallsofIvy

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    This isn't for a class? Do you know the derivative of eax?
     
  7. Nov 12, 2012 #6
    yes it is for a class. But, it is a practice problem. We haven't seen similar problems to this, so i am quite lost at the moment. I know the derivative of e^x is e^x.
     
  8. Nov 12, 2012 #7

    SammyS

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    Do you know the chain rule ?

    If so, use it ti find the derivative of eax, a being a constant.
     
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