What is the integral of (6/x+x/6) ?

The integral of (6/x+x/6) is 6ln|x|+(x^2)/(12)+C

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integral of (6/x+x/6)

\int (\frac{6}{x} + \frac{x}{6}) d x

6 ln ∣ x ∣ + \frac{x ^{2}}{12} + C

Solution steps

\int \frac{6}{x} + \frac{x}{6} 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{6}{x} d x + \int \frac{x}{6} d x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

\int \frac{x}{6} d x = \frac{x ^{2}}{12}

= 6 ln ∣ x ∣ + \frac{x ^{2}}{12}

Add a constant to the solution

= 6 ln ∣ x ∣ + \frac{x ^{2}}{12} + C

What is the integral of (6/x+x/6) ?
The integral of (6/x+x/6) is 6ln|x|+(x^2)/(12)+C