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Math Help - Integration by parts

  1. #1
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    Integration by parts

    How do you do this??? I know how to do integration by parts it's just this one problem...

    Evaluate the integral using integration by parts:
    The integral of (lnx)^2 dx (that's lnx squared)

    Thanks
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  2. #2
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    Lexington, MA (USA)
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    Hello, abcocoa!

    Did you try it at all? .There aren't many choices.


    ∫ (ln x) dx

    . . . . . . . . . . . . . . . . . . . . 2 ln x
    Let u .= .(ln x) . . du .= .------- dx
    . . . . . . . . . . . . . . . . . . . . . .x
    dv .= .dx . . v .= .x

    And we have: . x(ln x) - 2 ∫ ln x dx


    . . By parts again:

    . . . . u .= .ln x . . du .= .dx/x

    . . . . dv .= .dx/x . . v .= .x


    And we have: . x(ln x) - 2(xln x - ∫ dx) + C

    . . . . . . . . . . x(ln x) - 2xln x + 2x + C


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