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

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

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integral of x/((x^2))

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

ln ∣ x ∣ + C

Solution steps

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

Cancel the common factor:

x

= \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= ln ∣ x ∣

Add a constant to the solution

= ln ∣ x ∣ + C

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