256. ∫₁⁴ (x+√x)/√x dx.

Ответ: 6

\[\int_1^4 \frac{x + \sqrt{x}}{\sqrt{x}} dx = \int_1^4 (\frac{x}{\sqrt{x}} + 1) dx = \int_1^4 (\sqrt{x} + 1) dx = (\frac{2}{3} x^{3/2} + x) \vert_1^4 = (\frac{2}{3} \cdot 4^{3/2} + 4) - (\frac{2}{3} \cdot 1^{3/2} + 1) = (\frac{2}{3} \cdot 8 + 4) - (\frac{2}{3} + 1) = \frac{16}{3} + 4 - \frac{2}{3} - 1 = \frac{14}{3} + 3 = \frac{14 + 9}{3} = \frac{23}{3}\]

Ответ: 23/3