Answer
$-2(2-x)^{\frac{3}{2}} + \frac{2}{5}(2-x)^{\frac{5}{2}} +C$
Work Step by Step
Find the indefinite integral
Let $u=2-x$, $du= -dx$, $x=2-u$
$\int (x+1)\sqrt {2-x} dx$, Substitute
$-\int (3-u)u^{\frac{1}{2}}du$
$-\int(3u^{\frac{1}{2}} - u^{\frac{3}{2}})du$, Integrate
$-2u^{\frac{3}{2}} + \frac{2}{5}u^{\frac{5}{2}} +C$
$-2(2-x)^{\frac{3}{2}} + \frac{2}{5}(2-x)^{\frac{5}{2}} +C$
