>>94
lim[a→0]∫[a,e]2xlog(x)dx
=lim[a→0] ( [(x^2)log(x)][a,e] -∫[a,e](x^2)(1/x)dx)
=lim[a→0](e^2 - (a^2)log(a) -e^2/2 +a^2/2)
=e^2/2

lim[a→0]((a^2)log(a)) = lim[a→0](log(a)/(1/a^2))
=lim[a→0]((1/a)/(-2/a^3)) = 0