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Popular Calculus >

integral of 1+1/(x-1)

Solution

\int 1 + \frac{1}{x - 1} d x

Solution

x + ln ∣ x - 1 ∣ + C

Solution steps

\int 1 + \frac{1}{x - 1} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x + \int \frac{1}{x - 1} d x

\int 1 d x = x

\int \frac{1}{x - 1} d x = ln ∣ x - 1 ∣

= x + ln ∣ x - 1 ∣

Add a constant to the solution

= x + ln ∣ x - 1 ∣ + C

Graph

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Frequently Asked Questions (FAQ)

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