Question 107
Let $a$ be a positive real number. Find the value of $a$ such that the definite integral
$$
\int_{a}^{a^{2}} \frac{\mathrm{d} x}{x+\sqrt{x}}
$$
achieves its smallest possible value.
$$
\int_{a}^{a^{2}} \frac{\mathrm{d} x}{x+\sqrt{x}}
$$
achieves its smallest possible value.