Đáp án:
$P = \dfrac{16}{3}$
Giải thích các bước giải:
$\quad I = \displaystyle\int\limits_1^3\dfrac{dx}{\sqrt{x+1} -\sqrt x}$
$\Leftrightarrow I = \displaystyle\int\limits_1^3\dfrac{\sqrt{x+1} + \sqrt x}{\left(\sqrt{x+1} - \sqrt x\right)\left(\sqrt{x+1} + \sqrt x\right)}dx$
$\Leftrightarrow I = \displaystyle\int\limits_1^3\left(\sqrt{x+1} +\sqrt x\right)dx$
$\Leftrightarrow I = \left(\dfrac23\sqrt{(x+1)^3} + \dfrac23\sqrt{x^3}\right)\Bigg|_1^3$
$\Leftrightarrow I = 2\sqrt3 - \dfrac43\sqrt2 + \dfrac{14}{3}$
$\Rightarrow \begin{cases}a = 2\\b = -\dfrac43\\c = \dfrac{14}{3}\end{cases}$
$\Rightarrow a + b + c = 2 - \dfrac43 +\dfrac{14}{3}$
$\Rightarrow P = \dfrac{16}{3}$
