What is the integral of (7+sqrt(x)+x)/x ?

The integral of (7+sqrt(x)+x)/x is 7ln|x|+2sqrt(x)+x+C

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integral of (7+sqrt(x)+x)/x

\int \frac{7 + x + x}{x} d x

7 ln ∣ x ∣ + 2 x + x + C

Solution steps

\int \frac{7 + x + x}{x} d x

Expand

\frac{7 + x + x}{x} : \frac{7}{x} + \frac{1}{x} + 1

= \int \frac{7}{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{7}{x} d x + \int \frac{1}{x} d x + \int 1 d x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

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

\int 1 d x = x

= 7 ln ∣ x ∣ + 2 x + x

Add a constant to the solution

= 7 ln ∣ x ∣ + 2 x + x + C

\int_{- 1}^{2} \frac{∣ x ∣}{x} d x

f (x) = (4 x + 2)^{\frac{1}{4}}, at x = 1

\frac{\partial}{\partial x} (\frac{4}{4 x + y})

n = 1 \sum \infty \frac{2 n}{3}

\frac{\partial}{\partial x} (3 e^{y})

What is the integral of (7+sqrt(x)+x)/x ?
The integral of (7+sqrt(x)+x)/x is 7ln|x|+2sqrt(x)+x+C