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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{4} (ln (629) - 2 ln (2))

+1

Dezimale

1.26445 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{4}^{629} \frac{1}{4 u} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{4}^{629} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{4} [ln ∣ u ∣]_{4}^{629}

Berechne die Grenzen:

ln (629) - 2 ln (2)

= \frac{1}{4} (ln (629) - 2 ln (2))

Graph

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