integral from 0 to 2 of 4^{4x}

Lösung

\int_{0}^{2} 4^{4 x} d x

\frac{65535}{8 ln ( 2 )}

Dezimale

11818.37743 \dots

Schritte zur Lösung

\int_{0}^{2} 4^{4 x} d x

Vereinfache

4^{4 x} : 25 6^{x}

= \int_{0}^{2} 25 6^{x} d x

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

= [\frac{25 6 ^{x}}{ln ( 256 )}]_{0}^{2}

\frac{25 6 ^{x}}{ln ( 256 )} = \frac{2 ^{8 x - 3}}{ln ( 2 )}

= [\frac{2 ^{8 x - 3}}{ln ( 2 )}]_{0}^{2}

Berechne die Grenzen:

\frac{65535}{8 ln ( 2 )}

= \frac{65535}{8 ln ( 2 )}

\int_{0}^{1} (x + 4)^{10} d x

\int_{- 1}^{1} \frac{1}{x ^{4}} + \frac{1}{x - 4} d x

\int_{0}^{1} (4 t + 1)^{2} d t

\int_{1}^{2} (1 - x^{3}) d x

\int_{2}^{5} \frac{x}{x ^{2} - 4} d x