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  1. #1
    iva
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    Weird integral of e

    Hi there, I'm hoping someone can help me out. My textbook gives 1 example of this then the exercise gives a more complicated one so I'm not sure how to do it. Here goes..

    \int (2x+1)e^{x^2+x} = \int_{0}^{x}e^{t^2+t} dt + ce^{-x^2-x} ?

    Thanks!
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    Re: Weird integral of e

    Quote Originally Posted by iva View Post
    Hi there, I'm hoping someone can help me out. My textbook gives 1 example of this then the exercise gives a more complicated one so I'm not sure how to do it. Here goes..

    \int (2x+1)e^{x^2+x} = \int_{0}^{x}e^{t^2+t} dt + ce^{-x^2-x} ?

    Thanks!
    Let me give you a hint, in general what is \displaystyle \int u'(x) e^{u(x)}\;dx for a function u(x)?
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    iva
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    Re: Weird integral of e

    Is it e^u(x) + c ?
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    Re: Weird integral of e

    Quote Originally Posted by iva View Post
    Is it e^{u(x)} + c ?
    Look at the latex correction.
    [TEX]e^{u(x)} + c[/TEX] is e^{u(x)} + c
    correct.
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    iva
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    Re: Weird integral of e

    But what if it is not that simple that u'(x) is featured so perfectly on the left. For example what if they don't match up and you get something like

    \int (x+1)e^{-2x}

    Then I can't use that kind of reasoning can i?
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    MHF Contributor Drexel28's Avatar
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    Re: Weird integral of e

    Quote Originally Posted by iva View Post
    But what if it is not that simple that u'(x) is featured so perfectly on the left. For example what if they don't match up and you get something like

    \int (x+1)e^{-2x}

    Then I can't use that kind of reasoning can i?
    Well, in that case you need to try other methods--sometimes they aren't expressible in elementary terms (i.e. \displaystyle \int e^{x^2}\;dx). But, for this one it is that case, so it is that simple.
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    Re: Weird integral of e

    Quote Originally Posted by iva View Post
    But what if it is not that simple that u'(x) is featured so perfectly on the left. For example what if they don't match up and you get something like \int (x+1)e^{-2x}
    Then I can't use that kind of reasoning can i?
    That requires a completely different approach.
    You need integration by parts. That should come in about four additional sections in your textbook. Look it up.
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    iva
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    Re: Weird integral of e

    ok so this is one of the erf functions then right? But how do i combine it with doing integration by parts, as I think this is wrong as i ignored the (x+1) and copied the way the textbook example did a simpler example i.e.:


    \int (x+1)e^{-2x} = \int_{0}^{x} e^{-2t} dt + ce^{2x}
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    Re: Weird integral of e

    Quote Originally Posted by iva View Post
    ok so this is one of the erf functions then right? But how do i combine it with doing integration by parts, as I think this is wrong as i ignored the (x+1) and copied the way the textbook example did a simpler example i.e.: \int (x+1)e^{-2x} = \int_{0}^{x} e^{-2t} dt + ce^{2x}
    Either you copied incorrectly or your textbook means something else.
    \int (x+1)e^{-2x} = \frac{-x}{2}e^{-2x}-\frac{3}{4}e^{-2x}+c
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  10. #10
    iva
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    Re: Weird integral of e

    Quote Originally Posted by Plato View Post
    Either you copied incorrectly or your textbook means something else.
    \int (x+1)e^{-2x} = \frac{-x}{2}e^{-2x}-\frac{3}{4}e^{-2x}+c
    Crikey, ok so it was simply integration by parts.

    Thanks a mill
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