integral from 0 to 2 of 5^{2x}

Lösung

\int_{0}^{2} 5^{2 x} d x

\frac{312}{ln ( 5 )}

Dezimale

193.85649 \dots

Schritte zur Lösung

\int_{0}^{2} 5^{2 x} d x

Vereinfache

5^{2 x} : 2 5^{x}

= \int_{0}^{2} 2 5^{x} d x

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

= [\frac{2 5 ^{x}}{ln ( 25 )}]_{0}^{2}

Vereinfache

ln (25) : 2 ln (5)

= [\frac{2 5 ^{x}}{2 ln ( 5 )}]_{0}^{2}

Berechne die Grenzen:

\frac{312}{ln ( 5 )}

= \frac{312}{ln ( 5 )}

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