What is the integral from 5 to 25 of (x-5)/x ?

The integral from 5 to 25 of (x-5)/x is 20-5ln(5)

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integral from 5 to 25 of (x-5)/x

\int_{5}^{25} \frac{x - 5}{x} d x

20 - 5 ln (5)

Decimal

11.95281 \dots

Solution steps

\int_{5}^{25} \frac{x - 5}{x} d x

Expand

\frac{x - 5}{x} : 1 - \frac{5}{x}

= \int_{5}^{25} 1 - \frac{5}{x} 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_{5}^{25} 1 d x - \int_{5}^{25} \frac{5}{x} d x

\int_{5}^{25} 1 d x = 20

\int_{5}^{25} \frac{5}{x} d x = 5 ln (5)

= 20 - 5 ln (5)

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What is the integral from 5 to 25 of (x-5)/x ?
The integral from 5 to 25 of (x-5)/x is 20-5ln(5)