Need some help with simplification- Calculus

  • #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!
 

Answers and Replies

  • #2
1,101
3
((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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