What is the integral from 3 to 5 of (x-3)/(x-2) ?

The integral from 3 to 5 of (x-3)/(x-2) is -ln(3)+2

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integral from 3 to 5 of (x-3)/(x-2)

\int_{3}^{5} \frac{x - 3}{x - 2} d x

- ln (3) + 2

Decimal Notation

0.90138 \dots

Solution steps

\int_{3}^{5} \frac{x - 3}{x - 2} d x

\frac{x - 3}{x - 2} = - \frac{1}{x - 2} + 1

= \int_{3}^{5} - \frac{1}{x - 2} + 1 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_{3}^{5} \frac{1}{x - 2} d x + \int_{3}^{5} 1 d x

\int_{3}^{5} \frac{1}{x - 2} d x = ln (3)

\int_{3}^{5} 1 d x = 2

= - ln (3) + 2

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What is the integral from 3 to 5 of (x-3)/(x-2) ?
The integral from 3 to 5 of (x-3)/(x-2) is -ln(3)+2