What is the integral of (x^2-1)/(x^3-x) ?

The integral of (x^2-1)/(x^3-x) is ln|x|+C

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integral of (x^2-1)/(x^3-x)

\int \frac{x ^{2} - 1}{x ^{3} - x} d x

ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{2} - 1}{x ^{3} - x} d x

Simplify

\frac{x ^{2} - 1}{x ^{3} - x} : \frac{1}{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

What is the integral of (x^2-1)/(x^3-x) ?
The integral of (x^2-1)/(x^3-x) is ln|x|+C