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

\int \frac{cos ( x )}{1 + sin ( x )} d x

\frac{d}{d x} (x^{2} + 36)

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

\int (\frac{3}{u ^{2}} + \frac{4}{u ^{3}} - 2) d u

y^{^{''}} - 4 y^{^{'}} = sin (3 x)

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