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

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

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

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

x - 2 x + C

Solution steps

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

Expand

\frac{x - 1}{x} : 1 - \frac{1}{x}

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

\int 1 d x = x

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

= x - 2 x

Add a constant to the solution

= x - 2 x + C

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