Evaluate: integral of e^x+(1)/(e^x) x

Expression: $\int{ {e}^{x}+\frac{ 1 }{ {e}^{x} } } \mathrm{d} x$

Use the property of integral $\int{ f\left( x \right)\pmg\left( x \right) } \mathrm{d} x=\int{ f\left( x \right) } \mathrm{d} x\pm\int{ g\left( x \right) } \mathrm{d} x$

$\int{ {e}^{x} } \mathrm{d} x+\int{ \frac{ 1 }{ {e}^{x} } } \mathrm{d} x$

Use $\int{ {e}^{x} } \mathrm{d} x={e}^{x}$ to evaluate the integral

${e}^{x}+\int{ \frac{ 1 }{ {e}^{x} } } \mathrm{d} x$

Evaluate the indefinite integral

${e}^{x}-\frac{ 1 }{ {e}^{x} }$

Add the constant of integration $C \in ℝ$

$\begin{array} { l }{e}^{x}-\frac{ 1 }{ {e}^{x} }+C,& C \in ℝ\end{array}$