(3) $\\int\\left(e^{x}-\\frac{1}{x}\\right) d x$

Explanation:

Step1: Apply integral sum rule

$$\int\left(e^{x}-\frac{1}{x}\right) d x=\int e^{x} d x-\int\frac{1}{x} d x$$

Step2: Integrate each term

• For $\int e^{x} d x$, since the integral of $e^{x}$ with respect to $x$ is $e^{x}$.
• For $\int\frac{1}{x} d x$, the integral of $\frac{1}{x}$ with respect to $x$ is $\ln|x|$ (where $x\neq0$).

So, $\int e^{x} d x-\int\frac{1}{x} d x=e^{x}-\ln|x|+C$ ($C$ is the constant of integration)

Answer:

$e^{x}-\ln|x|+C$