Question

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

Answer 1

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

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

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

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

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