What is the integral of 9/(x-7) ?

The integral of 9/(x-7) is 9ln|x-7|+C

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integral of 9/(x-7)

\int \frac{9}{x - 7} d x

9 ln ∣ x - 7 ∣ + C

Solution steps

\int \frac{9}{x - 7} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int \frac{1}{x - 7} d x

Apply u-substitution

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

= 9 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 9 ln ∣ u ∣

Substitute back

u = x - 7

= 9 ln ∣ x - 7 ∣

Add a constant to the solution

= 9 ln ∣ x - 7 ∣ + C

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