Question:
$\int(1-x) \sqrt{x} d x$
Solution:
$\int(1-x) \sqrt{x} d x$
$=\int\left(\sqrt{x}-x^{\frac{3}{2}}\right) d x$
$=\int x^{\frac{1}{2}} d x-\int x^{\frac{3}{2}} d x$
$=\frac{x^{\frac{3}{2}}}{\frac{3}{2}}-\frac{x^{\frac{5}{2}}}{\frac{5}{2}}+\mathrm{C}$
$=\frac{2}{3} x^{\frac{3}{2}}-\frac{2}{5} x^{\frac{5}{2}}+\mathrm{C}$