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Popular Calculus >

integral of 3/x-x/3

Solution

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

Solution

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

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

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