What is the integral of (2-x)/(sqrt(x)) ?

The integral of (2-x)/(sqrt(x)) is 4sqrt(x)-2/3 x^{3/2}+C

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integral of (2-x)/(sqrt(x))

\int \frac{2 - x}{x} d x

4 x - \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{2 - x}{x} d x

Expand

\frac{2 - x}{x} : \frac{2}{x} - x

= \int \frac{2}{x} - x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2}{x} d x - \int x d x

\int \frac{2}{x} d x = 4 x

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

= 4 x - \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 4 x - \frac{2}{3} x^{\frac{3}{2}} + C

\frac{d}{d x} (cos^{2} (1 - x^{2}))

\frac{1 - 4 t}{3 + t}

\int \frac{( 2 z - 1 )}{2 z ^{2} - 6 z + 5} d z

(9 x + 1) y^{2} \frac{d y}{d x} + 4 x^{2} + 3 y^{3} = 0

\frac{d}{d x} (\frac{x ^{3.8}}{6 ^{x}})

What is the integral of (2-x)/(sqrt(x)) ?
The integral of (2-x)/(sqrt(x)) is 4sqrt(x)-2/3 x^{3/2}+C