integral from-4 to 2 of (x+5)/(x-3)

Lösung

\int_{- 4}^{2} \frac{x + 5}{x - 3} d x

- 8 ln (7) + 6

Dezimale

- 9.56728 \dots

Schritte zur Lösung

\int_{- 4}^{2} \frac{x + 5}{x - 3} d x

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

= \int_{- 4}^{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_{- 4}^{2} \frac{8}{x - 3} d x + \int_{- 4}^{2} 1 d x

\int_{- 4}^{2} \frac{8}{x - 3} d x = - 8 ln (7)

\int_{- 4}^{2} 1 d x = 6

= - 8 ln (7) + 6

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