Evaluate the integral: $\int (x^{\frac{3}{2}} + 2e^x - \frac{1}{x}) \, dx$

$\frac{2}{5}x^{5/2} + 2e^x - \ln |x| + C$

The correct answer is Option (4) → $\frac{2}{5}x^{5/2} + 2e^x - \ln |x| + C$

We have $\int (x^{\frac{3}{2}} + 2e^x - \frac{1}{x}) \, dx = \int x^{\frac{3}{2}} \, dx + \int 2e^x \, dx - \int \frac{1}{x} \, dx \text{}$

$= \frac{x^{\frac{3}{2} + 1}}{\frac{3}{2} + 1} + 2e^x - \log |x| + C \text{}$

$= \frac{2}{5} x^{\frac{5}{2}} + 2e^x - \log |x| + C \text{}$