What is the integral of 2/(5x)-3/(x^2) ?

The integral of 2/(5x)-3/(x^2) is 2/5 ln|x|+3/x+C

integral of 2/(5x)-3/(x^2)

\int \frac{2}{5 x} - \frac{3}{x ^{2}} d x

\frac{2}{5} ln ∣ x ∣ + \frac{3}{x} + C

Solution steps

\int \frac{2}{5 x} - \frac{3}{x ^{2}} 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{2}{5 x} d x - \int \frac{3}{x ^{2}} d x

\int \frac{2}{5 x} d x = \frac{2}{5} ln ∣ x ∣

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

= \frac{2}{5} ln ∣ x ∣ - (- \frac{3}{x})

Simplify

= \frac{2}{5} ln ∣ x ∣ + \frac{3}{x}

Add a constant to the solution

= \frac{2}{5} ln ∣ x ∣ + \frac{3}{x} + C

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What is the integral of 2/(5x)-3/(x^2) ?
The integral of 2/(5x)-3/(x^2) is 2/5 ln|x|+3/x+C