integral from 1 to 4 of 5^{3x}

Lösung

\int_{1}^{4} 5^{3 x} d x

\frac{244140500}{3 ln ( 5 )}

Dezimale

50564340.53028 \dots

Schritte zur Lösung

\int_{1}^{4} 5^{3 x} d x

Vereinfache

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

= \int_{1}^{4} 12 5^{x} d x

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

= [\frac{12 5 ^{x}}{ln ( 125 )}]_{1}^{4}

Vereinfache

ln (125) : 3 ln (5)

= [\frac{12 5 ^{x}}{3 ln ( 5 )}]_{1}^{4}

Berechne die Grenzen:

\frac{244140500}{3 ln ( 5 )}

= \frac{244140500}{3 ln ( 5 )}

\int_{1}^{8} \frac{4 x}{x ^{2} + 6} d x

\int_{2}^{4} (5 x^{3} + 2 x^{2} - 3 x - 8) d x

\int_{3}^{6} 15 ln (x + 5) d x

\int_{1}^{4} (2 x^{2} - 4 x + 5) d x

\int_{0}^{\frac{π}{4}} tan (t) d t