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

Lösung

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

\frac{1}{4} (ln (53) - ln (11))

Dezimale

0.39309 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{11}^{53} \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_{11}^{53} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{4} [ln ∣ u ∣]_{11}^{53}

Berechne die Grenzen:

ln (53) - ln (11)

= \frac{1}{4} (ln (53) - ln (11))

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