## Calculus 10th Edition

$\int$ $x^{2}\sqrt (1-x)$ $dx$ $=$ $\frac{-2}{3}$ $(1-x)^{3/2}$ $+$ $\frac{4}{5}$ $(1-x)^{5/2}$ $-$ $\frac{2}{7}$ $(1-x)^{7/2}$ $+$ $C$
$\int$ $x^{2}\sqrt (1-x)$ $dx$ $Let$ $U=1-x$ $,$ $dU=-dx$ $,$ $x=1-U$ $\int$ $x^{2}\sqrt (1-x)$ $dx$ $=$ $-\int(1-U)^{2}$ $U^{1/2}dU$ $=$ $-\int(1-2U+U^{2})$ $U^{1/2}dU$ $=$ $-\int(U^{1/2}-2U^{3/2}+U^{5/2})dU$ $=$ $-(\frac{U^{3/2}}{3/2}$ $-2$ $\frac{U^{5/2}}{5/2}$ $+$ $\frac{U^{7/2}}{7/2}$ $)$ $+$ $C$ $=$ $\frac{-2}{3}$ $U^{3/2}$ $+$ $\frac{4}{5}$ $U^{5/2}$ $-$ $\frac{2}{7}$ $U^{7/2}$ $+$ $C$ $=$ $\frac{-2}{3}$ $(1-x)^{3/2}$ $+$ $\frac{4}{5}$ $(1-x)^{5/2}$ $-$ $\frac{2}{7}$ $(1-x)^{7/2}$ $+$ $C$