What is the integral of (1/(x^2)+1/x) ?

The integral of (1/(x^2)+1/x) is -1/x+ln|x|+C

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integral of (1/(x^2)+1/x)

\int (\frac{1}{x ^{2}} + \frac{1}{x}) d x

- \frac{1}{x} + ln ∣ x ∣ + C

Solution steps

\int \frac{1}{x ^{2}} + \frac{1}{x} 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{1}{x ^{2}} d x + \int \frac{1}{x} d x

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{1}{x} + ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{x} + ln ∣ x ∣ + C

\int x + C d x

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What is the integral of (1/(x^2)+1/x) ?
The integral of (1/(x^2)+1/x) is -1/x+ln|x|+C