Evaluate the integral $\int{(2x+3)}\sqrt{x-4}dx=I$

Evaluate the integral $\int{(2x+3)}\sqrt{x-4}dx=I$

Let $3=-8+11$

$\therefore$, $I=\int{(2x-8+11)}\sqrt{x-4} dx$. 

$=\int{[2(x-4)}+11]\sqrt{x-4}dx$. 

$2\int{(x-4)}^{\frac{3}{2}}dx+11\int{(x-4)}^\frac{1}{2}dx$. 

$=\frac{4}{5}(x-4)^\frac{5}{2}+\frac{22}{3}(x-4)^\frac{3}{2}+C$.