integral from 0 to 5 of (3x+11)/(x+2)

Lösung

\int_{0}^{5} \frac{3 x + 11}{x + 2} d x

- 5 ln (2) + 5 ln (7) + 15

Dezimale

21.26381 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{3 x + 11}{x + 2} d x

Multipliziere aus

\frac{3 x + 11}{x + 2} : \frac{3 x}{x + 2} + \frac{11}{x + 2}

Wende die Summenregel an:

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

= \int_{0}^{5} \frac{3 x}{x + 2} d x + \int_{0}^{5} \frac{11}{x + 2} d x

\int_{0}^{5} \frac{3 x}{x + 2} d x = 3 (5 - 2 (ln (7) - ln (2)))

\int_{0}^{5} \frac{11}{x + 2} d x = 11 (ln (7) - ln (2))

= 3 (5 - 2 (ln (7) - ln (2))) + 11 (ln (7) - ln (2))

Vereinfache

3 (5 - 2 (ln (7) - ln (2))) + 11 (ln (7) - ln (2)) : - 5 ln (2) + 5 ln (7) + 15

= - 5 ln (2) + 5 ln (7) + 15

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