What is the integral of 12+(500)/(x+1) ?

The integral of 12+(500)/(x+1) is 12x+500ln|x+1|+C

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integral of 12+(500)/(x+1)

\int 12 + \frac{500}{x + 1} d x

12 x + 500 ln ∣ x + 1 ∣ + C

Solution steps

\int 12 + \frac{500}{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 12 d x + \int \frac{500}{x + 1} d x

\int 12 d x = 12 x

\int \frac{500}{x + 1} d x = 500 ln ∣ x + 1 ∣

= 12 x + 500 ln ∣ x + 1 ∣

Add a constant to the solution

= 12 x + 500 ln ∣ x + 1 ∣ + C

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What is the integral of 12+(500)/(x+1) ?
The integral of 12+(500)/(x+1) is 12x+500ln|x+1|+C