Question

Find the integral of $\int (1+x)\sqrt{x}dx$

Answer 1

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

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

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

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

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