Answer
$\frac{2}{5}(x+6)^{\frac{5}{2}} - 4(x+6)^{\frac{3}{2}} +C$
Work Step by Step
Find the indefinite integral.
To use the steps from Example 5, let $u=x+6$, then $du=dx$, and $x=u-6$
$\int x\sqrt {x+6} dx$
Substitute for the terms under the radical, and for the x outside the radical
$\int (u-6)u^{\frac{1}{2}}du$, Substitute
$\int (u^{\frac{3}{2}} -6u^{\frac{1}{2}})du$
$\frac{2}{5}u^{\frac{5}{2}} - 4u^{\frac{3}{2}} +C$, Integrate
$\frac{2}{5}(x+6)^{\frac{5}{2}} - 4(x+6)^{\frac{3}{2}} +C$
