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

(5, - 4), (7, - 4)

\int \frac{e ^{\frac{1}{t}}}{t ^{2}} d t

\frac{d}{d x} (2 x^{2} - x)

\frac{2 s + 16}{s ^{2} + 4 s + 13}

- 18 x^{2} y^{^{''}} + 4 x (x + 9) y^{^{'}} - 4 (x + 9) y = - 4 x^{3}

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