What is the integral from 0 to 1 of-1/(x-5)+2/(x-2) ?

The integral from 0 to 1 of-1/(x-5)+2/(x-2) is -4ln(2)+ln(5)

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integral from 0 to 1 of-1/(x-5)+2/(x-2)

\int_{0}^{1} - \frac{1}{x - 5} + \frac{2}{x - 2} d x

- 4 ln (2) + ln (5)

Decimal

- 1.16315 \dots

Solution steps

\int_{0}^{1} - \frac{1}{x - 5} + \frac{2}{x - 2} 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}^{1} \frac{1}{x - 5} d x + \int_{0}^{1} \frac{2}{x - 2} d x

\int_{0}^{1} \frac{1}{x - 5} d x = 2 ln (2) - ln (5)

\int_{0}^{1} \frac{2}{x - 2} d x = - 2 ln (2)

= - (2 ln (2) - ln (5)) - 2 ln (2)

Simplify

= - 4 ln (2) + ln (5)

What is the integral from 0 to 1 of-1/(x-5)+2/(x-2) ?
The integral from 0 to 1 of-1/(x-5)+2/(x-2) is -4ln(2)+ln(5)