Answer
$\frac{1}{15}(10x(x-5)^\frac{3}{2}-4(x-5)^\frac{5}{2})+C$
Work Step by Step
Given $\int x\sqrt {x-5}$.
You can use the Tabular Method.
Derivative | Anti-derivative
(+)$x|\sqrt {x-5}$
(-)$1|\frac{2}{3}(x-5)^\frac{3}{2}$
(+)$0|\frac{4}{15}(x-5)^\frac{5}{2}$
$=\frac{2}{3}x(x-5)^\frac{3}{2}-\frac{4}{15}(x-5)^\frac{5}{2}+C$
$=\frac{1}{15}(10x(x-5)^\frac{3}{2}-4(x-5)^\frac{5}{2})+C$
