What is the integral of (sqrt(x)+1)/x ?

The integral of (sqrt(x)+1)/x is 2sqrt(x)+ln|x|+C

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integral of (sqrt(x)+1)/x

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

2 x + ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= 2 x + ln ∣ x ∣

Add a constant to the solution

= 2 x + ln ∣ x ∣ + C

y^{4}

(2 sin (t))^{^{'}}

x \to 2 lim (x^{2} + 7 - x)

\frac{\partial}{\partial x} (y^{4} + 5 x y^{3})

\frac{d}{d x} (cos (5 x - 3))

What is the integral of (sqrt(x)+1)/x ?
The integral of (sqrt(x)+1)/x is 2sqrt(x)+ln|x|+C