# How do you integrate int (sqrtx+1/(2sqrtx))dx?

Dec 21, 2016

$\frac{2}{3} {x}^{\frac{3}{2}} + {x}^{\frac{1}{2}} + C$

#### Explanation:

Start by simplifying the equation.

$\implies \int \left({x}^{\frac{1}{2}}\right) \mathrm{dx} + \int \left(\frac{1}{2} {x}^{- \frac{1}{2}}\right) \mathrm{dx}$

Use the formula ${x}^{n} \mathrm{dx} = \frac{{x}^{n + 1}}{n + 1} + C$

$\implies \frac{2}{3} {x}^{\frac{3}{2}} + \frac{1}{2} \int \left({x}^{- \frac{1}{2}}\right) \mathrm{dx}$

You don't have to add $+ C$ just yet... It should be alright if you add that once you have integrated all terms.

$\implies \frac{2}{3} {x}^{\frac{3}{2}} + \frac{1}{2} \left(2 {x}^{\frac{1}{2}}\right) + C$

$\implies \frac{2}{3} {x}^{\frac{3}{2}} + {x}^{\frac{1}{2}} + C$

Hopefully this helps!