integrate k*x*e^(d*x)

Indefinite integral

integral k x e^(d x) dx = (k e^(d x) (d x - 1))/d^2 + constant

Series expansion of the integral at x=0

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