Question

Evaluate: $\int (1-x)\sqrt{x}dx.$

Answer 1

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

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

$=\int \sqrt{x}dx-\int x^{\frac{3}{2}}dx$

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

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