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Math Help - Tricky Integration

  1. #1
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    Tricky Integration

    Could anyone help me integrate the following equation;

    e^(x+y) + ln(x) + (e^(x+y) + y^2)dy/dx = 0


    I can see it is exact and in the form P(x,y) + Q(x,y)dy/dx=0 and so I should be able to solve it using the partial differentiation method, but that would mean integrating ln x with respect to x, which I thought was impossible.

    Many thanks.
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  2. #2
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    Quote Originally Posted by hairymclairy View Post
    ... but that would mean integrating ln x with respect to x, which I thought was impossible.
    \int \ln{x} \, dx = x(\ln{x} - 1) + C
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  3. #3
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    Thanks, I've never seen that result before. Which is slightly disconcerting.
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  4. #4
    Moo
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    Quote Originally Posted by hairymclairy View Post
    Thanks, I've never seen that result before. Which is slightly disconcerting.
    You can easily get this result by an integration by parts :

    \int \ln(x) ~dx
    u=ln(x)
    dv=1
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