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

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

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integral of (x/3-3/x)

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

\frac{x ^{2}}{6} - 3 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{x ^{2}}{6} - 3 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{6} - 3 ln ∣ x ∣ + C

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