integral from 0 to ln(3) of x/(x^2-3x)

Lösung

\int_{0}^{l n (3)} \frac{x}{x ^{2} - 3 x} d x

ln (- ln (3) + 3) - ln (3)

Dezimale

- 0.45602 \dots

Schritte zur Lösung

\int_{0}^{l n (3)} \frac{x}{x ^{2} - 3 x} d x

Faktorisiere

\frac{x}{x ^{2} - 3 x}

= \int_{0}^{l n (3)} \frac{x}{x ( x - 3 )} d x

Streiche die gemeinsamen Faktoren:

x

= \int_{0}^{l n (3)} \frac{1}{x - 3} d x

Wende U-Substitution an

= \int_{- 3}^{l n (3) - 3} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{- 3}^{l n (3) - 3}

Berechne die Grenzen:

ln (- ln (3) + 3) - ln (3)

= ln (- ln (3) + 3) - ln (3)

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