integral from-1 to 2 of 5^{3x}

Lösung

\int_{- 1}^{2} 5^{3 x} d x

\frac{1953124}{375 ln ( 5 )}

Dezimale

3236.11779 \dots

Schritte zur Lösung

\int_{- 1}^{2} 5^{3 x} d x

Vereinfache

5^{3 x} : 12 5^{x}

= \int_{- 1}^{2} 12 5^{x} d x

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

= [\frac{12 5 ^{x}}{ln ( 125 )}]_{- 1}^{2}

Vereinfache

ln (125) : 3 ln (5)

= [\frac{12 5 ^{x}}{3 ln ( 5 )}]_{- 1}^{2}

Berechne die Grenzen:

\frac{1953124}{375 ln ( 5 )}

= \frac{1953124}{375 ln ( 5 )}

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