integral from 0 to 5 of x/(3x^2+6)

Lösung

\int_{0}^{5} \frac{x}{3 x ^{2} + 6} d x

\frac{1}{6} ln (\frac{27}{2})

Dezimale

0.43378 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{x}{3 x ^{2} + 6} d x

Wende U-Substitution an

= \int_{6}^{81} \frac{1}{6 u} d u

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{6}^{81} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} [ln ∣ u ∣]_{6}^{81}

Berechne die Grenzen:

4 ln (3) - ln (6)

= \frac{1}{6} (4 ln (3) - ln (6))

Vereinfache

= \frac{1}{6} ln (\frac{27}{2})

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