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Simple integral

  1. May 9, 2005 #1
    My brain is truly fried.

    I know this:
    [tex] \int e^u du = e^u +C [/tex]

    But what do I do if I get this:
    [tex] \int ae^a^u du [/tex] ? Assuming a is a non-zero constant?

    EDIT: Never mind! I figured this out backwards.

    [tex] \frac {d}{du} e^a^u = ae^a^u du[/tex]

    Thus

    [tex] \int ae^a^u du = e^a^u [/tex]
     
    Last edited: May 9, 2005
  2. jcsd
  3. May 9, 2005 #2
    You can use substitution.
    [tex]y=au\Rightarrow \frac{dy}{du}=a\Rightarrow du=\frac{dy}{a}[/tex]
    Therefore,
    [tex]\int ae^{au}du=\int ae^{y}\frac{1}{a}dy=\int e^{y}dy=e^{y}+C=e^{au}+C[/tex]
     
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