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

\int (e^{2 x} cos (e^{2 x})) d x

\frac{d}{d x} (\frac{1}{x ^{2}} + \frac{1}{x ^{3}})

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

f (t) = \frac{t ^{2} - 4}{t - 2}

\frac{6}{x ^{2}}

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