What is the integral from 1 to 3 of (x-3)/x ?

The integral from 1 to 3 of (x-3)/x is 2-3ln(3)

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integral from 1 to 3 of (x-3)/x

\int_{1}^{3} \frac{x - 3}{x} d x

2 - 3 ln (3)

Decimal Notation

- 1.29583 \dots

Solution steps

\int_{1}^{3} \frac{x - 3}{x} d x

Expand

\frac{x - 3}{x} : 1 - \frac{3}{x}

= \int_{1}^{3} 1 - \frac{3}{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_{1}^{3} 1 d x - \int_{1}^{3} \frac{3}{x} d x

\int_{1}^{3} 1 d x = 2

\int_{1}^{3} \frac{3}{x} d x = 3 ln (3)

= 2 - 3 ln (3)

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What is the integral from 1 to 3 of (x-3)/x ?
The integral from 1 to 3 of (x-3)/x is 2-3ln(3)