Answer
$\frac{2}{45}(3x-4)^{\frac{5}{2}}+\frac{8}{27}(3x-4)^{\frac{3}{2}}+C$
Work Step by Step
Find the indefinite integral using the same method from Example 5
Let $u=3x-4$, $,x=\frac{u+4}{3}$, and $du=3dx$
$\int x\sqrt {3x-4}dx$
$\frac{1}{3}\int \frac{u+4}{3}u^{\frac{1}{2}}du$, substitute
$\frac{1}{9} \int (u^{\frac{3}{2}} +4u^{\frac{1}{2}})du$, Integrate
$\frac{1}{9}(\frac{2}{5}u^{\frac{5}{2}} +\frac{8}{3}u^{\frac{3}{2}})+C$
$\frac{2}{45}(3x-4)^{\frac{5}{2}}+\frac{8}{27}(3x-4)^{\frac{3}{2}}+C$
