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

Question

$\begin{array}{1 1}(A)\; (x-1)e^{x+\large\frac{1}{x}}+c \\ (B)\; xe^{x+\large\frac{1}{x}}+c \\ (C)\; (x+1)e^{x+\large\frac{1}{x}}+c \\ (D) -xe^{x+\large\frac{1}{x}}+c\end{array} $