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

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

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

\int (\frac{x + 2}{x}) d x

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

f (x) = 3 x + 4, at x = 7

\int_{3}^{4} \frac{1}{( x - 3 ) ^{3}} d x

f (x) = 3 x^{- 2}, at x = 4

x \to + 0 lim (1 + sinh (2 x))

\frac{d y}{d x} = \frac{6 x}{5 y}

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