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

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

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

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

- ln (3) + 2

Decimal

0.90138 \dots

Solution steps

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

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

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

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}{y - 2} d y + \int_{3}^{5} 1 d y

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

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

= - ln (3) + 2

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