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Beliebt Rechnen >

integral from-1 to 3 of x/(x^2+4)

Lösung

\int_{- 1}^{3} \frac{x}{x ^{2} + 4} d x

Lösung

\frac{1}{2} (ln (13) - ln (5))

+1

Dezimale

0.47775 \dots

Schritte zur Lösung

\int_{- 1}^{3} \frac{x}{x ^{2} + 4} d x

Wende U-Substitution an

= \int_{5}^{13} \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_{5}^{13} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{5}^{13}

Berechne die Grenzen:

ln (13) - ln (5)

= \frac{1}{2} (ln (13) - ln (5))

Graph

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