Решить интеграл. [latex] \int\limits^3_0 { \frac{1}{2 \sqrt{x+1} } } \, dx[/latex]

[latex] \int\frac{1}{2 \sqrt{x + 1}} \, dx = \int{ \frac{1}{2 \sqrt{x + 1}} } \,d(x +1) = \int{ \frac{1}{2 \sqrt{u}}} \, du = \int{ \frac{1}{2}u^{-1/2} \,du = \frac{1}{2}2u^{1/2} +c = \sqrt{x + 1} + c \int\limits^3_0 \frac{1}{2 \sqrt{x + 1}} \, dx = \sqrt{3+1} - \sqrt{0+1} = 2 -1 =1[/latex] [/latex]