Answer
$=\frac{2}{3}x^{\frac{3}{2}} + 12x^{\frac{1}{2}} + C$
Work Step by Step
$\int (\frac{x+6}{\sqrt {x}})dx$
$\int (\frac{x}{x^{\frac{1}{2}}} + \frac{6}{\sqrt {x}})dx$
$\int (x^{1-\frac{1}{2}}) + 6x^{-\frac{1}{2}}dx$
$\int (x^{\frac{1}{2}}) + 6x^{-\frac{1}{2}}dx$
$= \frac{x^{\frac{3}{2}}}{\frac{3}{2}} + \frac{6x^{\frac{1}{2}}}{\frac{1}{2}} + C$
$= (x^{\frac{3}{2}} \times \frac{2}{3}) + (6x^{\frac{1}{2}} \times 2) + C$
$=\frac{2}{3}x^{\frac{3}{2}} + 12x^{\frac{1}{2}} + C$
