What is the integral of 18-(54)/(15-2x) ?

The integral of 18-(54)/(15-2x) is 18x+27ln|15-2x|+C

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integral of 18-(54)/(15-2x)

\int 18 - \frac{54}{15 - 2 x} d x

18 x + 27 ln ∣ 15 - 2 x ∣ + C

Solution steps

\int 18 - \frac{54}{15 - 2 x} 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 18 d x - \int \frac{54}{15 - 2 x} d x

\int 18 d x = 18 x

\int \frac{54}{15 - 2 x} d x = - 27 ln ∣ 15 - 2 x ∣

= 18 x - (- 27 ln ∣ 15 - 2 x ∣)

Simplify

= 18 x + 27 ln ∣ 15 - 2 x ∣

Add a constant to the solution

= 18 x + 27 ln ∣ 15 - 2 x ∣ + C

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What is the integral of 18-(54)/(15-2x) ?
The integral of 18-(54)/(15-2x) is 18x+27ln|15-2x|+C