What is the integral of 50-(20)/(x+5) ?

The integral of 50-(20)/(x+5) is 50x-20ln|x+5|+C

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integral of 50-(20)/(x+5)

\int 50 - \frac{20}{x + 5} d x

50 x - 20 ln ∣ x + 5 ∣ + C

Solution steps

\int 50 - \frac{20}{x + 5} 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 50 d x - \int \frac{20}{x + 5} d x

\int 50 d x = 50 x

\int \frac{20}{x + 5} d x = 20 ln ∣ x + 5 ∣

= 50 x - 20 ln ∣ x + 5 ∣

Add a constant to the solution

= 50 x - 20 ln ∣ x + 5 ∣ + C

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What is the integral of 50-(20)/(x+5) ?
The integral of 50-(20)/(x+5) is 50x-20ln|x+5|+C