The integral $\;\int (1+x-\large\frac{1}{x})\;e^{x+\large\frac{1}{x}} dx\;$ is equal to :

Question

$(a)\;(x+1) e^{x+\large\frac{1}{x}} +c \qquad(b)\;-xe^{x+\large\frac{1}{x}} +c \qquad(c)\;(x-1) e^{x+\large\frac{1}{x}} +c \qquad(d)\;x e^{x+\large\frac{1}{x}} +c $