Question

Find the following integral: $\int (1-x)\sqrt xdx$

Answer 1

$\int (1-x)\sqrt xdx$

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

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

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

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