integral from 0 to 2 of (e^{3y}-3)/(e^{3y)-9y+18}

Lösung

\int_{0}^{2} \frac{e ^{3 y} - 3}{e ^{3 y} - 9 y + 18} d y

\frac{1}{3} (6 - ln (19))

Dezimale

1.01852 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{e ^{3 y} - 3}{e ^{3 y} - 9 y + 18} d y

Wende U-Substitution an

= \int_{19}^{e^{6}} \frac{1}{3 u} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{19}^{e^{6}} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} [ln ∣ u ∣]_{19}^{e^{6}}

Berechne die Grenzen:

6 - ln (19)

= \frac{1}{3} (6 - ln (19))

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