Question

Find the integral of $\int \sqrt{x}(3x^2+2x+3)dx$

Answer 1

$\int \sqrt{x}(3x^2+2x+3)dx$
$=\int (3x^{\frac{5}{2}}+2x^{\frac{3}{2}}+3x^{\frac{1}{2}})dx$
$=3\int x^{\frac{5}{2}}dx+2\int x^{\frac{3}{2}}dx+3\int x^{\frac{1}{2}}dx$
$=3\left(\frac{x^{\frac{7}{2}}}{\frac{7}{2}}\right)+2\left(\frac{x^{\frac{5}{2}}}{\frac{5}{2}}\right)+3\left(\frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right)+C$
$=\frac{6}{7}{x}^{\frac{7}{2}}+\frac{4}{5}{x}^{\frac{5}{2}}+2x^{\frac{3}{2}}+C$