The integral ∫ (1 + x - (1)/(x))e^ x + (1)/(x) dx is equal to

We have,&

$I = ∫ \left(1 + x - \dfrac{1}{x}\right)e^{x + \dfrac{1}{x}}dx$

$I = ∫ e^{x + \dfrac{1}{x}}dx + ∫ \left(x - \dfrac{1}{x}\right)e^{x + \dfrac{1}{x}}dx$

$I = ∫ e^{x + \dfrac{1}{x}}dx + ∫ x\left(1 - \dfrac{1}{x2}\right)e^{x + \dfrac{1}{x}}dx$

$I = ∫ e^{x + \dfrac{1}{x}}dx + xe^{x + \dfrac{1}{x}} - ∫ e^{x + \dfrac{1}{x}}dx$

$I = xe^{x + \dfrac{1}{x}} + C$