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

The integral of (2/x+x/2) is 2ln|x|+(x^2)/4+C

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integral of (2/x+x/2)

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

2 ln ∣ x ∣ + \frac{x ^{2}}{4} + C

Solution steps

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ + \frac{x ^{2}}{4}

Add a constant to the solution

= 2 ln ∣ x ∣ + \frac{x ^{2}}{4} + C

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What is the integral of (2/x+x/2) ?
The integral of (2/x+x/2) is 2ln|x|+(x^2)/4+C