Indefinite Integration

$(x+1) e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)

$-x e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)

$(x-1) e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)

$x e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)