The integral $\begin{align*} \int \begin{pmatrix}1 + x - \frac{1}{x} \end{pmatrix} e^{x + \frac{1}{x}} dx \end{align*}$ is equal to

Question

( A ) $-x e^{^{x+\frac{1}{x}}}+c$
( B ) $(x-1) e^{^{x+\frac{1}{x}}}+c$
( C ) $x e^{^{x+\frac{1}{x}}}+c$
( D ) $(x+1) e^{^{x+\frac{1}{x}}}+c$