int(e^(1/Q)*(1 -1/Q),Q)

Indefinite integral

integral e^(1/Q) (1 - 1/Q) dQ = e^(1/Q) Q + constant

Plot

Plot
Plot

Series expansion of the integral at Q=∞

Q + 1 + 1/(2 Q) + 1/(6 Q^2) + O((1/Q)^3)
(Laurent series)