What is the integral from 100 to 200 of 5+3/(x+2) ?

The integral from 100 to 200 of 5+3/(x+2) is 500+3ln(101/51)

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integral from 100 to 200 of 5+3/(x+2)

\int_{100}^{200} 5 + \frac{3}{x + 2} d x

500 + 3 ln (\frac{101}{51})

Decimal

502.04988 \dots

Solution steps

\int_{100}^{200} 5 + \frac{3}{x + 2} 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_{100}^{200} 5 d x + \int_{100}^{200} \frac{3}{x + 2} d x

\int_{100}^{200} 5 d x = 500

\int_{100}^{200} \frac{3}{x + 2} d x = 3 ln (\frac{101}{51})

= 500 + 3 ln (\frac{101}{51})

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What is the integral from 100 to 200 of 5+3/(x+2) ?
The integral from 100 to 200 of 5+3/(x+2) is 500+3ln(101/51)