What is the integral from 2 to infinity of 1/(v^2+5v-6) ?

The integral from 2 to infinity of 1/(v^2+5v-6) is 3/7 ln(2)

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integral from 2 to infinity of 1/(v^2+5v-6)

\int_{2}^{\infty} \frac{1}{v ^{2} + 5 v - 6} d v

\frac{3}{7} ln (2)

Decimal

0.29706 \dots

Solution steps

\int_{2}^{\infty} \frac{1}{v ^{2} + 5 v - 6} d v

Compute the indefinite integral:

\int \frac{1}{v ^{2} + 5 v - 6} d v = \frac{1}{7} ln ∣ v - 1 ∣ - \frac{1}{7} ln ∣ v + 6 ∣ + C

Compute the boundaries:

\int_{2}^{\infty} \frac{1}{v ^{2} + 5 v - 6} d v = 0 - (- \frac{3}{7} ln (2))

= 0 - (- \frac{3}{7} ln (2))

Simplify

= \frac{3}{7} ln (2)

What is the integral from 2 to infinity of 1/(v^2+5v-6) ?
The integral from 2 to infinity of 1/(v^2+5v-6) is 3/7 ln(2)