What is the integral of (x^2+3)/(sqrt(x)) ?

The integral of (x^2+3)/(sqrt(x)) is 2/5 x^{5/2}+6sqrt(x)+C

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integral of (x^2+3)/(sqrt(x))

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

\frac{2}{5} x^{\frac{5}{2}} + 6 x + C

Solution steps

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

Expand

\frac{x ^{2} + 3}{x} : x^{\frac{3}{2}} + \frac{3}{x}

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

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

\int \frac{3}{x} d x = 6 x

= \frac{2}{5} x^{\frac{5}{2}} + 6 x

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} + 6 x + C

2 x (5 - 4 x)^{4}, at x = 1

(- 3 x y^{2} + 5 y) + (- 3 x^{2} y + 5 x) y^{^{'}} = 0

\frac{d}{d x} ((x^{2} - 4)^{\frac{1}{2}})

\int p^{2} d p

x \to - 2 lim (\frac{1}{x + 2})

What is the integral of (x^2+3)/(sqrt(x)) ?
The integral of (x^2+3)/(sqrt(x)) is 2/5 x^{5/2}+6sqrt(x)+C