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

The integral of ((x-1))/(sqrt(x)) is 2/3 x^{3/2}-2sqrt(x)+C

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

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

\frac{2}{3} x^{\frac{3}{2}} - 2 x + C

Solution steps

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

Expand

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

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

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

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

= \frac{2}{3} x^{\frac{3}{2}} - 2 x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} - 2 x + C

\frac{d}{d x} (ln (x + 3 + x^{2}))

x \to 0 lim (\frac{( x ^{3} + 3 x )}{x})

- 8 x^{2} y + y^{^{'}} = - 5 x^{2}

\int \frac{1}{3 - 4 sin ^{2} ( x )} d x

f (x) = x^{2020}

What is the integral of ((x-1))/(sqrt(x)) ?
The integral of ((x-1))/(sqrt(x)) is 2/3 x^{3/2}-2sqrt(x)+C