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Math Help - Integral help needed.

  1. #1
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    Integral help needed.

    I get stuck on this one.

    \displaystyle{ \int 8 x e^{2 x^2} \, dx}
    <br />
u=2x^2

    du=4x

    8 \int 4x{e}^{u}

    \frac{8}{4}\int du{e}^{u}

    \frac{1}{2}\int du{e}^{u}

    My final answer was:

    \frac{1}{2}{e}^{2x^2}

    But I feel it's wrong.

    This natural number always screws me up.
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  2. #2
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    Quote Originally Posted by Zanderist View Post
    I get stuck on this one.

    \displaystyle{ \int 8 x e^{2 x^2} \, dx}
    <br />
u=2x^2

    du=4x \, dx

    2 \int 4x{e}^{2x^2} \, dx ... fixed this

    2 \int e^u \, du ... and this.
    finish it.
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  3. #3
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    Why does the 8 turn into a 2?
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  4. #4
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    Quote Originally Posted by Zanderist View Post
    I get stuck on this one.

    \displaystyle{ \int 8 x e^{2 x^2} \, dx}
    <br />
u=2x^2

    du=4xdx => dx = du/4x

    2 \int 4x{e}^{u}du/4x

    2 \int {e}^{u}du

    [snip]

    My final answer was:

    2 {e}^{2x^2}

    But I feel it's wrong. Mr F says: Yes it was.

    This natural number always screws me up.
    I have made corrections and annotations in red. If you were not so sloppy with your notation you probably would not have made all these mistakes.
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  5. #5
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    Quote Originally Posted by Zanderist View Post
    Why does the 8 turn into a 2?
    the 8 turned into 2 times 4 ... not 2.

    then, note that 4x \, dx changed to du
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  6. #6
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    Quote Originally Posted by skeeter View Post
    the 8 turned into 2 times 4 ... not 2.
    Ah!

    Thanks everyone.
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