integral from 0 to ln(3) of xe^{3x}

Lösung

\int_{0}^{l n (3)} x e^{3 x} d x

\frac{1}{9} (81 ln (3) - 26)

Dezimale

6.99862 \dots

Schritte zur Lösung

\int_{0}^{l n (3)} x e^{3 x} d x

Wende U-Substitution an

= \int_{0}^{3 l n (3)} \frac{e ^{u} u}{9} d u

Entferne die Konstante:

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

= \frac{1}{9} \cdot \int_{0}^{3 l n (3)} e^{u} u d u

Wende die partielle Integration an

= \frac{1}{9} [e^{u} u - \int e^{u} d u]_{0}^{3 l n (3)}

\int e^{u} d u = e^{u}

= \frac{1}{9} [e^{u} u - e^{u}]_{0}^{3 l n (3)}

Berechne die Grenzen:

81 ln (3) - 26

= \frac{1}{9} (81 ln (3) - 26)

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