What is the integral of ((x+9)/(sqrt(x))) ?

The integral of ((x+9)/(sqrt(x))) is 2/3 x^{3/2}+18sqrt(x)+C

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integral of ((x+9)/(sqrt(x)))

\int (\frac{x + 9}{x}) d x

\frac{2}{3} x^{\frac{3}{2}} + 18 x + C

Solution steps

\int \frac{x + 9}{x} d x

Expand

\frac{x + 9}{x} : x + \frac{9}{x}

= \int x + \frac{9}{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{9}{x} d x

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

\int \frac{9}{x} d x = 18 x

= \frac{2}{3} x^{\frac{3}{2}} + 18 x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + 18 x + C

y^{^{''}} + 2 y^{^{'}} + y = 3 e^{- x} x + 1

f (t) = ln (t^{2} + 1)

n = 6 \sum \infty e^{3 - 2 n}

x^{2} y^{^{''}} + x y^{^{'}} = 0

\frac{d}{d x} (3 x^{2} lo g_{3} (x))

What is the integral of ((x+9)/(sqrt(x))) ?
The integral of ((x+9)/(sqrt(x))) is 2/3 x^{3/2}+18sqrt(x)+C