# Find the following integral. \int \frac{3-x}{\sqrt{x}}dx

Find the following integral.
$\int \frac{3-x}{\sqrt{x}}dx$
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jlo2niT
Given that
$\int \frac{3-x}{\sqrt{x}}dx$
$=3\int \frac{1}{\sqrt{x}}dx-\int \sqrt{x}dx$
$=3\left[\frac{{x}^{\frac{-1}{2}+1}}{\frac{-1}{2}+1}\right]-\left[\frac{{x}^{\frac{1}{2}+1}}{\frac{1}{2}+1}\right]+C$
$=3\left(2\sqrt{x}\right)-\frac{2}{3}\cdot {x}^{\frac{3}{2}}+C$
$\therefore \int \frac{3-x}{\sqrt{x}}dx=6\sqrt{x}-\frac{2}{3}\cdot {x}^{\frac{3}{2}}+C$