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

Lösung

\int_{0}^{e} \frac{x}{x ^{2} + e} d x

\frac{1}{2} (ln (e^{2} + e) - 1)

Dezimale

0.65663 \dots

Schritte zur Lösung

\int_{0}^{e} \frac{x}{x ^{2} + e} d x

Wende U-Substitution an

= \int_{e}^{e^{2} + e} \frac{1}{2 u} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{e}^{e^{2} + e} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{e}^{e^{2} + e}

Berechne die Grenzen:

ln (e^{2} + e) - 1

= \frac{1}{2} (ln (e^{2} + e) - 1)

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