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Need confirmation on this integration problem!

  1. Apr 23, 2005 #1

    jzq

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    Here's the problem:
    [tex]\int e^{(5x)}[/tex]

    This is what I got (Correct me if I am wrong.):
    [tex]\frac{1}{5}e^{(5x)}[/tex]

    Or is it just the same:
    [tex]e^{(5x)}[/tex]
     
  2. jcsd
  3. Apr 23, 2005 #2

    OlderDan

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    You are sort of right. I think you mean

    [tex]\int e^{(5x)}dx = \frac{1}{5}e^{(5x)} + c[/tex]
     
  4. Apr 23, 2005 #3

    jzq

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    Yes, I forgot to add the constant, but that's what I meant.
    So I am correct then?
     
  5. Apr 23, 2005 #4
    Yeah. In general, if you want to check yourself, just take the derivative of what you just integrated. If you get back the integrand, then you know you solved it correctly.
     
  6. Apr 23, 2005 #5
    Linearity of primitive functions:

    [tex]
    \int f(x)\ dx = F(x)\ +\ C \Rightarrow \int f(ax)\ dx = \frac{1}{a} F(ax)\ +\ C,\ a \in \mathbb{R}\ \backslash \ \{0\}
    [/tex]
     
  7. Apr 23, 2005 #6

    jzq

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    Thanks guys!
     
  8. Apr 23, 2005 #7

    OlderDan

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    You also forgot to include the variable of integration for your integral. You need to know what the integration variable is. It will not always be dx, so you should be careful with it.
     
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