Problem

Use algebraic integration and the substitution $u=\sqrt{x}$ to find the exact value of

$$\int_1^4 \frac{10}{5x+2x\sqrt{x}}\,dx$$

Write your answer in the form $4\ln\left(\dfrac{a}{b}\right)$, where $a$ and $b$ are integers to be found.

(Solutions relying entirely on calculator technology are not acceptable.)