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

The integral of (1/(2x)-2/(x^2)+3/(sqrt(x))) is 1/2 ln|x|+2/x+6sqrt(x)+C

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integral of (1/(2x)-2/(x^2)+3/(sqrt(x)))

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

\frac{1}{2} ln ∣ x ∣ + \frac{2}{x} + 6 x + C

Solution steps

\int \frac{1}{2 x} - \frac{2}{x ^{2}} + \frac{3}{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 \frac{1}{2 x} d x - \int \frac{2}{x ^{2}} d x + \int \frac{3}{x} d x

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

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

\int \frac{3}{x} d x = 6 x

= \frac{1}{2} ln ∣ x ∣ - (- \frac{2}{x}) + 6 x

Simplify

= \frac{1}{2} ln ∣ x ∣ + \frac{2}{x} + 6 x

Add a constant to the solution

= \frac{1}{2} ln ∣ x ∣ + \frac{2}{x} + 6 x + C

10 t^{\frac{6}{5}} + 6 e^{3}

\frac{d y}{d x} = y + 8

\frac{d}{d x} (x^{\frac{1}{3}} (x + 8))

\frac{\partial}{\partial z} (x yz + x y^{2} + y z^{2} + z x^{2})

What is the integral of (1/(2x)-2/(x^2)+3/(sqrt(x))) ?
The integral of (1/(2x)-2/(x^2)+3/(sqrt(x))) is 1/2 ln|x|+2/x+6sqrt(x)+C