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Popular Calculus >

integral of 1/(v-1)

Solution

\int \frac{1}{v - 1} d v

Solution

ln ∣ v - 1 ∣ + C

Solution steps

\int \frac{1}{v - 1} d v

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = v - 1

= ln ∣ v - 1 ∣

Add a constant to the solution

= ln ∣ v - 1 ∣ + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 1/(v-1) ?
The integral of 1/(v-1) is ln|v-1|+C