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Popular Calculus >

integral of 1/(y-5)

Solution

\int \frac{1}{y - 5} d y

Solution

ln ∣ y - 5 ∣ + C

Solution steps

\int \frac{1}{y - 5} d y

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 = y - 5

= ln ∣ y - 5 ∣

Add a constant to the solution

= ln ∣ y - 5 ∣ + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 1/(y-5) ?
The integral of 1/(y-5) is ln|y-5|+C