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Math Help - integral (3+2x^2)/xdx

  1. #1
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    integral (3+2x^2)/xdx

    how would one solve this?
    I used integration by parts and got

    (3+2x^2)lnx - 1/2x^2lnx - 1/4x^2

    it's a differential equation os

    1/3y^3 = (3+2x^2)lnx - 1/2x^2lnx - 1/4x^2 where y(1) = 0
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  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
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    Quote Originally Posted by khuezy View Post
    how would one solve this?
    I used integration by parts and got

    (3+2x^2)lnx - 1/2x^2lnx - 1/4x^2

    it's a differential equation os

    1/3y^3 = (3+2x^2)lnx - 1/2x^2lnx - 1/4x^2 where y(1) = 0
    By parts is not required, you can do it this way...
    \int \frac{3+2x^2}{x} \, dx = \int \left(\frac{3}{x}+2x\right)\, dx = 3\ln x + x^2 +C
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  3. #3
    Flow Master
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    Quote Originally Posted by Isomorphism View Post
    By parts is not required, you can do it this way...
    \int \frac{3+2x^2}{x} \, dx = \int \left(\frac{3}{x}+2x\right)\, dx = 3\ln x + x^2 +C
    *Ahem* 3\ln {\color{red}|}x{\color{red}|} + x^2 +C
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