What is the integral from 0 to 5 of (50)/(x+5)-5 ?

The integral from 0 to 5 of (50)/(x+5)-5 is 50ln(2)-25

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integral from 0 to 5 of (50)/(x+5)-5

\int_{0}^{5} \frac{50}{x + 5} - 5 d x

50 ln (2) - 25

Decimal

9.65735 \dots

Solution steps

\int_{0}^{5} \frac{50}{x + 5} - 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_{0}^{5} \frac{50}{x + 5} d x - \int_{0}^{5} 5 d x

\int_{0}^{5} \frac{50}{x + 5} d x = 50 ln (2)

\int_{0}^{5} 5 d x = 25

= 50 ln (2) - 25

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What is the integral from 0 to 5 of (50)/(x+5)-5 ?
The integral from 0 to 5 of (50)/(x+5)-5 is 50ln(2)-25