Question

Write the anti-derivative of $(3\sqrt{x}+\frac{1}{\sqrt{x}})$.

Answer 1

Anti-derivative of $(3\sqrt{x}+\frac{1}{\sqrt{x}})$

$=\int (3\sqrt{x}+\frac{1}{\sqrt{x}})dx$

$=3\left(\frac{x^{1/2+1}}{1/2+1}\right)+\left[\frac{x^{-1/2+1}}{-1/2+1}\right]+C$

$=2(x^{3/2}+x^{1/2})+C$