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

The integral of (9+sqrt(x)+x)/x is 9ln|x|+2sqrt(x)+x+C

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

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

9 ln ∣ x ∣ + 2 x + x + C

Solution steps

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

Expand

\frac{9 + x + x}{x} : \frac{9}{x} + \frac{1}{x} + 1

= \int \frac{9}{x} + \frac{1}{x} + 1 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{9}{x} d x + \int \frac{1}{x} d x + \int 1 d x

\int \frac{9}{x} d x = 9 ln ∣ x ∣

\int \frac{1}{x} d x = 2 x

\int 1 d x = x

= 9 ln ∣ x ∣ + 2 x + x

Add a constant to the solution

= 9 ln ∣ x ∣ + 2 x + x + C

n = 1 \sum \infty arctan (19 n)

\int - 4 x^{2} sin (π x) d x

f (x) = 5 x + 1, at x = 3

\frac{\partial}{\partial x} (x - 3 y^{2} + 4 x^{2} y^{3})

4 x^{2} + 5

What is the integral of (9+sqrt(x)+x)/x ?
The integral of (9+sqrt(x)+x)/x is 9ln|x|+2sqrt(x)+x+C