Question

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

Answer 1

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

$=\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}-\frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1}$

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