Question

Integrate:

$\int \frac{{\left(x+a\right)}^2}{\sqrt{x}}dx$

Answer 1

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

$=\int \frac{x^2+2ax+a^2}{\sqrt{x}}dx$

$=\int (x^{3/2}+2a{x}^{1/2}+a^2{x}^{-1/2})dx$

$=\frac{2x^{5/2}}{5}+\frac{2}{3}\cdot 2a{x}^{3/2}+2\cdot a^2{x}^{1/2}+C$