integral from 0 to 3 of 5^xln(5)

Lösung

\int_{0}^{3} 5^{x} ln (5) d x

124

Schritte zur Lösung

\int_{0}^{3} 5^{x} ln (5) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= ln (5) \cdot \int_{0}^{3} 5^{x} d x

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

= ln (5) [\frac{5 ^{x}}{ln ( 5 )}]_{0}^{3}

Berechne die Grenzen:

\frac{124}{ln ( 5 )}

= ln (5) \frac{124}{ln ( 5 )}

Vereinfache

= 124

\int_{1}^{3} \frac{x ^{2} - 2}{x + 1} d x

\int_{0}^{5} 25 cos (\frac{π}{10} x) d x

\int_{- \infty}^{120} (2 - x) d x

\int_{- 1}^{1} e^{x} sin (2 x) d x

\int_{0}^{3} (x e^{2 x}) d x