What is the integral of 10-(100)/(x+10) ?

The integral of 10-(100)/(x+10) is 10x-100ln|x+10|+C

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integral of 10-(100)/(x+10)

\int 10 - \frac{100}{x + 10} d x

10 x - 100 ln ∣ x + 10 ∣ + C

Solution steps

\int 10 - \frac{100}{x + 10} 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 10 d x - \int \frac{100}{x + 10} d x

\int 10 d x = 10 x

\int \frac{100}{x + 10} d x = 100 ln ∣ x + 10 ∣

= 10 x - 100 ln ∣ x + 10 ∣

Add a constant to the solution

= 10 x - 100 ln ∣ x + 10 ∣ + C

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What is the integral of 10-(100)/(x+10) ?
The integral of 10-(100)/(x+10) is 10x-100ln|x+10|+C