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This is a really old question, but the answers omit a significant fact.

Let us say that w = %e^x/x-(%e^x-1)/x^2. As computed here (DERIV ...)

From the given construction we know that ONE anti-derivative of w is (exp(x)-1)/x; but there are an infinite number of anti-derivatives. remember your calculus ... + a constant.

From Maxima we know (in the absence of bugs etc) that another anti-derivative is

-1/x-gamma_incomplete(0,-x)-gamma_incomplete(-1,-x)

They don't have to be the same.

They can differ by a constant. As it happens, they don't. But they could.