integral from 0 to log_{9 of (4)}9^x

Lösung

\int_{0}^{l o g_{9} (4)} 9^{x} d x

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

Dezimale

1.36535 \dots

Schritte zur Lösung

\int_{0}^{l o g_{9} (4)} 9^{x} d x

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

= [\frac{9 ^{x}}{ln ( 9 )}]_{0}^{l o g_{9} (4)}

Vereinfache

[\frac{9 ^{x}}{ln ( 9 )}]_{0}^{l o g_{9} (4)} : [\frac{9 ^{x}}{2 ln ( 3 )}]_{0}^{2 l o g_{9} (2)}

= [\frac{9 ^{x}}{2 ln ( 3 )}]_{0}^{2 l o g_{9} (2)}

Berechne die Grenzen:

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

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

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