integrate x exp(ax) dx

Indefinite integral

integral x exp(a x) dx = (e^(a x) (a x - 1))/a^2 + constant

Series expansion of the integral at x=0

-1/a^2 + x^2/2 + (a x^3)/3 + (a^2 x^4)/8 + O(x^5)
(Taylor series)