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Math Help - antiderivative

  1. #1
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    antiderivative

    (integral symbol) (7e^(2x)-3e^-x) dx

    Thanks guys i dont know how to do it with the e's
    Last edited by Chris L T521; July 23rd 2009 at 12:31 PM. Reason: Restored original question.
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  2. #2
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     \int e^{ax} dx = \frac{e^{ax}}{a}+c
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jwbehm View Post
    (integral symbol) (7e^(2x)-3e^-x) dx

    Thanks guys i dont know how to do it with the e's
    Break it up first

    7\int{e^{2x}}-3\int{e}^{-x}

    In the first let u_1=2x, then \frac{1}{2}du_1=dx

    In the second let u_2=-x, then -du_2=dx
    (Iwrite subscripts to avoid confusion, I should have used u AND v, but too late now)...
    and we have

    \frac{7}{2}\int{e^{u_1}}du_1+3\int{e^{u_2}}du_2

    The integral of e^u:e^u

    Therefore (subbing back for u)

    =\frac{7}{2}e^{2x}+3e^{-x}+C
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by jwbehm View Post
    thanks.
    Deleting your question after receiving help is not allowed. It shows us that you are hiding something that you shouldn't be receiving help on.

    Thread Closed.
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