Cho ∫ 0 1 1/ x+2 + x+1 dx = ab - 8/3a+2/3 (a,b∈ℕ*) .Tính a + 2b

Câu hỏi :

Cho ${\int }_0^1\frac{1}{\sqrt{x+2} + \sqrt{x+1}}dx = a\sqrt{b} - \frac{8}{3}\sqrt{a}+\frac{2}{3} (a,b\in {\mathrm{\mathbb{N}}}^{*})$ .Tính a + 2b