What is the integral of (3/x+x/3) ?

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

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integral of (3/x+x/3)

\int (\frac{3}{x} + \frac{x}{3}) d x

3 ln ∣ x ∣ + \frac{x ^{2}}{6} + C

Solution steps

\int \frac{3}{x} + \frac{x}{3} 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{3}{x} d x + \int \frac{x}{3} d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{x}{3} d x = \frac{x ^{2}}{6}

= 3 ln ∣ x ∣ + \frac{x ^{2}}{6}

Add a constant to the solution

= 3 ln ∣ x ∣ + \frac{x ^{2}}{6} + C

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