integral from 0 to 1 of (2x^4)/(3x^5+20)

Lösung

\int_{0}^{1} \frac{2 x ^{4}}{3 x ^{5} + 20} d x

\frac{2}{15} (ln (23) - ln (20))

Dezimale

0.01863 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{2 x ^{4}}{3 x ^{5} + 20} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{1} \frac{x ^{4}}{3 x ^{5} + 20} d x

Wende U-Substitution an

= 2 \cdot \int_{20}^{23} \frac{1}{15 u} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{15} \cdot \int_{20}^{23} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 \cdot \frac{1}{15} [ln ∣ u ∣]_{20}^{23}

Vereinfache

2 \cdot \frac{1}{15} [ln ∣ u ∣]_{20}^{23} : \frac{2}{15} [ln ∣ u ∣]_{20}^{23}

= \frac{2}{15} [ln ∣ u ∣]_{20}^{23}

Berechne die Grenzen:

ln (23) - ln (20)

= \frac{2}{15} (ln (23) - ln (20))

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