Question

Find the following integrals:
$\int (1-x)\sqrt{x}dx$.

Answer 1

$I=\int (1-x)\sqrt{x}dx$

$=\int \sqrt{x}-x\sqrt{x}dx$

$=\int (x{)}^{1/2}-(x{)}^{3/2}dx$

$=\frac{x^{3/2}}{3/2}-\frac{x^{5/2}}{5/2}+c$

$=\frac{2}{3}{x}^{3/2}-\frac{2}{5}{x}^{5/2}+c$.