Evaluate: `int (1-x)sqrt(x)\ dx`

Explanation

`int(1-{x}) sqrt{{x}} {dx}=`

`int(sqrt{{x}}-{x} sqrt{{x}}) {dx}`

`=int({x} frac{1}{2}-{x} frac{3}{2}) {dx}`

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

`=frac{2}{3} x^{frac{3}{2}}-frac{2}{5} x^{frac{5}{2}}+c`, C is integral constant.

`(`because `int {x}^{n} {dx}=(frac{x^{n+1}}{n+1}))`

`int(1-{x}) sqrt{{x}} {d} {x}=frac{2}{3} x^{frac{3}{2}}-frac{2}{5} x^{frac{5}{2}}+{c}`