integral from 0 to 1 of 2^{3x}

Lösung

\int_{0}^{1} 2^{3 x} d x

\frac{7}{3 ln ( 2 )}

Dezimale

3.36628 \dots

Schritte zur Lösung

\int_{0}^{1} 2^{3 x} d x

Vereinfache

2^{3 x} : 8^{x}

= \int_{0}^{1} 8^{x} d x

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

= [\frac{8 ^{x}}{ln ( 8 )}]_{0}^{1}

Vereinfache

ln (8) : 3 ln (2)

= [\frac{8 ^{x}}{3 ln ( 2 )}]_{0}^{1}

Berechne die Grenzen:

\frac{7}{3 ln ( 2 )}

= \frac{7}{3 ln ( 2 )}

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