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Need some help with simplification- Calculus

  1. Feb 17, 2010 #1
    I have found for the integral of x(lnx)^2 dx to be :
    ((1)/(4)x^2)(2(ln(x)-1)ln(x)+1)

    but i need it to be in one of these forms:
    these are the choices:
    x^2((lnx)^2 + lnx- (1/2)) +C
    1/2 x^2 ((lnx)^2 +lnx + 1/2) +C
    x^2((lnx)^2 + lnx + (1/2)) + C
    x^2((lnx)^2 - lnx + (1/2)) + C
    1/2 x^2 ((lnx)^2 -lnx + 1/2) +C
    1/2 x^2 ((lnx)^2 -lnx - 1/2) +C

    Thanks!
     
  2. jcsd
  3. Feb 18, 2010 #2
    ((1)/(4)x^2)(2(ln(x)-1)ln(x)+1) = (1/2)x^2[(ln(x) - 1)ln(x) + 1/2] = 1/2 x^2 ((lnx)^2 -lnx + 1/2), so

    1/2 x^2 ((lnx)^2 -lnx + 1/2) +C

    is the correct choice.
     
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