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

The integral of (sqrt(x)-x/2+2/(sqrt(x))) is 2/3 x^{3/2}-(x^2)/4+4sqrt(x)+C

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integral of (sqrt(x)-x/2+2/(sqrt(x)))

\int (x - \frac{x}{2} + \frac{2}{x}) d x

\frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{4} + 4 x + C

Solution steps

\int x - \frac{x}{2} + \frac{2}{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{x}{2} d x + \int \frac{2}{x} d x

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

\int \frac{2}{x} d x = 4 x

= \frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{4} + 4 x

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{4} + 4 x + C

What is the integral of (sqrt(x)-x/2+2/(sqrt(x))) ?
The integral of (sqrt(x)-x/2+2/(sqrt(x))) is 2/3 x^{3/2}-(x^2)/4+4sqrt(x)+C