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

Lösung

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

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

Dezimale

0.80471 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{10} \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_{2}^{10} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{2}^{10}

Berechne die Grenzen:

ln (10) - ln (2)

= \frac{1}{2} (ln (10) - ln (2))

Vereinfache

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

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