Answer
$\frac{2}{5}$ $(4-x)^{\frac{5}{2}}$ - $\frac{8}{3}$$(4-x)^{\frac{3}{2}}$ + $c$
Work Step by Step
$u$ = $4-x$
$du$ = $-dx$
$u$ = $4-x$
$so$
$x$ = $4-u$
$\int$ $x$ $\sqrt{4-x}$ $dx$ = -$\int$ $(4-u)$ $u^{\frac{1}{2}}$ $du$
= $\int$ $(u^{\frac{3}{2}}$ - $4u^{\frac{1}{2}})$ $du$
= $\frac{2}{5}$ $u^{\frac{5}{2}}$ - $\frac{8}{3}$$u^{\frac{3}{2}}$ + $c$
= $\frac{2}{5}$ $(4-x)^{\frac{5}{2}}$ - $\frac{8}{3}$$(4-x)^{\frac{3}{2}}$ + $c$
