Integrate ((ln(x))^2)/x^3 using a u-substitution and then integration by parts.

Answer 1

f=(lnx)^2 g'= 1/x f'=2lnx/x, g= -1/x^2

integral of fg' = fg - integral of gf'

integral of [ln(x)]^2/x^2 dx

= -[(lnx)^2+2lnx +2]/x + C