Answer
$$\frac{{14}}{3}$$
Work Step by Step
$$\eqalign{
& \int_0^5 {\frac{x}{{\sqrt {4 + x} }}} dx \cr
& {\text{Integrate by tables, use }}\int {\frac{u}{{\sqrt {a + bu} }}} = \frac{{ - 2\left( {2a - bu} \right)}}{{3{b^2}}}\sqrt {a + bu} + C \cr
& \int_0^5 {\frac{x}{{\sqrt {4 + x} }}} dx = \left[ {\frac{{ - 2\left( {2\left( 4 \right) - x} \right)}}{{3{{\left( 1 \right)}^2}}}\sqrt {4 + x} } \right]_0^5 \cr
& = - \frac{2}{3}\left[ {\left( {8 - x} \right)\sqrt {4 + x} } \right]_0^5 \cr
& {\text{Evaluate}} \cr
& = - \frac{2}{3}\left[ {\left( {8 - 5} \right)\sqrt {4 + 5} } \right] + \frac{2}{3}\left[ {\left( {8 - 0} \right)\sqrt {4 + 0} } \right] \cr
& = - \frac{2}{3}\left[ 9 \right] + \frac{2}{3}\left[ {16} \right] \cr
& = \frac{{14}}{3} \cr} $$
