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Beliebt Rechnen >

integral from 0 to ln(2) of 3e^{3x}

Lösung

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

Lösung

7

Schritte zur Lösung

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

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{l n (2)} e^{3 x} d x

Wende U-Substitution an

= 3 \cdot \int_{0}^{3 l n (2)} e^{u} \frac{1}{3} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{3} \cdot \int_{0}^{3 l n (2)} e^{u} d u

Nutze das gemeinsame Integral :

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

= 3 \cdot \frac{1}{3} [e^{u}]_{0}^{3 l n (2)}

Vereinfache

3 \cdot \frac{1}{3} [e^{u}]_{0}^{3 l n (2)} : [e^{u}]_{0}^{3 l n (2)}

= [e^{u}]_{0}^{3 l n (2)}

Berechne die Grenzen:

7

= 7

Graph

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