integral from 0 to 1 of 3^xe^x

Lösung

\int_{0}^{1} 3^{x} e^{x} d x

\frac{3 e - 1}{ln ( 3 e )}

Dezimale

3.40932 \dots

Schritte zur Lösung

\int_{0}^{1} 3^{x} e^{x} d x

Wende Exponentenregel an:

a^{n} \cdot b^{n} = (a \cdot b)^{n}

3^{x} e^{x} = (3 e)^{x}

= \int_{0}^{1} (3 e)^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= [\frac{( 3 e ) ^{x}}{ln ( 3 e )}]_{0}^{1}

Berechne die Grenzen:

\frac{3 e - 1}{ln ( 3 e )}

= \frac{3 e - 1}{ln ( 3 e )}

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