What is the integral from 2 to infinity of 3/(x^2-x) ?

The integral from 2 to infinity of 3/(x^2-x) is 3ln(2)

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integral from 2 to infinity of 3/(x^2-x)

\int_{2}^{\infty} \frac{3}{x ^{2} - x} d x

3 ln (2)

Decimal

2.07944 \dots

Solution steps

\int_{2}^{\infty} \frac{3}{x ^{2} - x} d x

Compute the indefinite integral:

\int \frac{3}{x ^{2} - x} d x = 3 (- ln ∣ x ∣ + ln ∣ x - 1 ∣) + C

Compute the boundaries:

\int_{2}^{\infty} \frac{3}{x ^{2} - x} d x = 0 - (- 3 ln (2))

= 0 - (- 3 ln (2))

Simplify

= 3 ln (2)

What is the integral from 2 to infinity of 3/(x^2-x) ?
The integral from 2 to infinity of 3/(x^2-x) is 3ln(2)