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

Lösung

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

\frac{2}{3} ln (3)

Dezimale

0.73240 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{9} \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_{1}^{9} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{1}^{9}

Berechne die Grenzen:

2 ln (3)

= \frac{1}{3} \cdot 2 ln (3)

Vereinfache

= \frac{2}{3} ln (3)

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