Question

Integrate:$\int \sqrt{2x}$dx

Answer 1

$\int \sqrt{2x}dx$

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

$=\sqrt{2}\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}$

$=\sqrt{2}\frac{x^{\frac{3}{2}}}{\frac{3}{2}}$

$=\frac{2\sqrt{2}x\sqrt{x}}{3}+c$

$=\frac{2x\sqrt{2x}}{3}+c$ where $c$ is the constant of integration.