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Math Help - partial integral of e^xy

  1. #1
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    partial integral of e^xy

    not sure if that title makes sense...

    here's the problem i need to solve
    find the integral of: (ye^xy)dx

    so since i'm integrating with respect to x, i first just tack on an x, to get:

    xye^xy. right?

    now i need to divide by the derivative of xy, since e^xy. this is where i'm stuck. since i'm integrating only with x, does that mean i take the partial derivative of xy with respect to x? leaving me with just y.

    so then i'd end up with xe^xy. is that the right answer?
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  2. #2
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    Quote Originally Posted by isuckatcalc View Post
    not sure if that title makes sense...

    here's the problem i need to solve
    find the integral of: (ye^xy)dx

    so since i'm integrating with respect to x, i first just tack on an x, to get:

    xye^xy. right?

    now i need to divide by the derivative of xy, since e^xy. this is where i'm stuck. since i'm integrating only with x, does that mean i take the partial derivative of xy with respect to x? leaving me with just y.

    so then i'd end up with xe^xy. is that the right answer?
    I assume you can integrate something like 2 e^{2x} .... ? Or even k e^{kx} ....? This is no different. y is treated as a constant. The required integral is e^{yx}. Differentiate this result to see if it's still unclear.
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  3. #3
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    this is my third attempt to reply... odd problems

    the derivative of e^xy is (e^xy)/y. correct?

    so that'd cancel out the y in the numerator and leave me with xe^xy, as i originally thought. i'm still not sure that's the right answer though.
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  4. #4
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    nevermind, i got it now. thanks for the help
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  5. #5
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    Quote Originally Posted by isuckatcalc View Post
    this is my third attempt to reply... odd problems

    the derivative of e^xy is (e^xy)/y. correct?

    so that'd cancel out the y in the numerator and leave me with xe^xy, as i originally thought. i'm still not sure that's the right answer though.
    No! Do you know how to differentiate e^{2x}? Have you been taught a formula for differentiating e^{kx}?

    If y is treated as a constant and x is the variable then the derivative of e^{yx} is y e^{yx}.
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  6. #6
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    yeah, i was completely overthinking the problem. thanks for your help, i did get it, unfortunately not until after i made my first reply to the post.
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