1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook