integral from 0 to 1 of (2x-2)/(x+3)

Lösung

\int_{0}^{1} \frac{2 x - 2}{x + 3} d x

2 - 8 (2 ln (2) - ln (3))

Dezimale

- 0.30145 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{2 x - 2}{x + 3} d x

Wende U-Substitution an

= \int_{3}^{4} \frac{2 u - 8}{u} d u

Multipliziere aus

\frac{2 u - 8}{u} : 2 - \frac{8}{u}

= \int_{3}^{4} 2 - \frac{8}{u} d u

Wende die Summenregel an:

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

= \int_{3}^{4} 2 d u - \int_{3}^{4} \frac{8}{u} d u

\int_{3}^{4} 2 d u = 2

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

= 2 - 8 (2 ln (2) - ln (3))

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