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

$\frac{3}{5} x^{\frac{5}{3}} + x + C$

The correct answer is Option (1) → $\frac{3}{5} x^{\frac{5}{3}} + x + C$

We have

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

$= \frac{x^{\frac{2}{3} + 1}}{\frac{2}{3} + 1} + x + C = \frac{3}{5} x^{\frac{5}{3}} + x + C \text{}$