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

\frac{\partial}{\partial y} (x^{2} + y^{2} + 10)

sin (7 x)

\frac{d}{d x} (\frac{1}{2 + x ^{2}})

t^{2} y^{^{''}} + 11 t y^{^{'}} + 25 y = 0, y (1) = 4, y^{^{'}} (1) = 9

\int 18 - \frac{54}{15 - 2 x} d x

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