integral from 0 to 3 of (12)/(3x+1)

Lösung

\int_{0}^{3} \frac{12}{3 x + 1} d x

4 ln (10)

Dezimale

9.21034 \dots

Schritte zur Lösung

\int_{0}^{3} \frac{12}{3 x + 1} d x

Entferne die Konstante:

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

= 12 \cdot \int_{0}^{3} \frac{1}{3 x + 1} d x

Wende U-Substitution an

= 12 \cdot \int_{1}^{10} \frac{1}{3 u} d u

Entferne die Konstante:

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

= 12 \cdot \frac{1}{3} \cdot \int_{1}^{10} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 12 \cdot \frac{1}{3} [ln ∣ u ∣]_{1}^{10}

Vereinfache

12 \cdot \frac{1}{3} [ln ∣ u ∣]_{1}^{10} : 4 [ln ∣ u ∣]_{1}^{10}

= 4 [ln ∣ u ∣]_{1}^{10}

Berechne die Grenzen:

ln (10)

= 4 ln (10)

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