What is the integral of (5/x-x/5) ?

The integral of (5/x-x/5) is 5ln|x|-(x^2)/(10)+C

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integral of (5/x-x/5)

\int (\frac{5}{x} - \frac{x}{5}) d x

5 ln ∣ x ∣ - \frac{x ^{2}}{10} + C

Solution steps

\int \frac{5}{x} - \frac{x}{5} 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{5}{x} d x - \int \frac{x}{5} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int \frac{x}{5} d x = \frac{x ^{2}}{10}

= 5 ln ∣ x ∣ - \frac{x ^{2}}{10}

Add a constant to the solution

= 5 ln ∣ x ∣ - \frac{x ^{2}}{10} + C

What is the integral of (5/x-x/5) ?
The integral of (5/x-x/5) is 5ln|x|-(x^2)/(10)+C