What is the integral of 15+(200)/(x+1) ?

The integral of 15+(200)/(x+1) is 15x+200ln|x+1|+C

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integral of 15+(200)/(x+1)

\int 15 + \frac{200}{x + 1} d x

15 x + 200 ln ∣ x + 1 ∣ + C

Solution steps

\int 15 + \frac{200}{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 15 d x + \int \frac{200}{x + 1} d x

\int 15 d x = 15 x

\int \frac{200}{x + 1} d x = 200 ln ∣ x + 1 ∣

= 15 x + 200 ln ∣ x + 1 ∣

Add a constant to the solution

= 15 x + 200 ln ∣ x + 1 ∣ + C

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What is the integral of 15+(200)/(x+1) ?
The integral of 15+(200)/(x+1) is 15x+200ln|x+1|+C