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

Lösung

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

- 24 ln (2) + 7

Dezimale

- 9.63553 \dots

Schritte zur Lösung

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

\frac{x + 5}{x - 3} = \frac{8}{x - 3} + 1

= \int_{- 5}^{2} \frac{8}{x - 3} + 1 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 5}^{2} \frac{8}{x - 3} d x + \int_{- 5}^{2} 1 d x

\int_{- 5}^{2} \frac{8}{x - 3} d x = - 24 ln (2)

\int_{- 5}^{2} 1 d x = 7

= - 24 ln (2) + 7

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