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

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

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

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

2 x - x + C

Solution steps

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

Expand

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

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

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

\int 1 d x = x

= 2 x - x

Add a constant to the solution

= 2 x - x + C

\frac{10 lo g _{4} ( t )}{t}

\int - 2 x 8 - x^{2} d x

x \to 0 + lim (\frac{x - ∣ x ∣}{x})

x \to \infty lim (ln (3 x) - ln (x + 7))

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

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