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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{3} (ln (7) - 2 ln (2))

+1

Dezimale

0.18653 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{4}^{7} \frac{1}{3 u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{4}^{7} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{4}^{7}

Berechne die Grenzen:

ln (7) - 2 ln (2)

= \frac{1}{3} (ln (7) - 2 ln (2))

Graph

Beliebte Beispiele

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