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

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

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integral from 2 to infinity of 2/(v^2-v)

\int_{2}^{\infty} \frac{2}{v ^{2} - v} d v

2 ln (2)

Decimal

1.38629 \dots

Solution steps

\int_{2}^{\infty} \frac{2}{v ^{2} - v} d v

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 2 ln (2))

Simplify

= 2 ln (2)

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