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

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

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

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

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

Solution steps

\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} (e^{2^{x}})

d x + e^{- 5 x} d y = 0

f (x) = 2 ln (6 + x)

\frac{d}{d x} (\frac{3}{lo g _{8} ( x )})

x \cdot y^{^{'}} - y = \frac{5}{4} \cdot x \cdot ln (x)

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