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

Lösung

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

\frac{1023}{5 ln ( 2 )}

Dezimale

295.17540 \dots

Schritte zur Lösung

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

Vereinfache

2^{5 x} : 3 2^{x}

= \int_{0}^{2} 3 2^{x} d x

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

= [\frac{3 2 ^{x}}{ln ( 32 )}]_{0}^{2}

Vereinfache

ln (32) : 5 ln (2)

= [\frac{3 2 ^{x}}{5 ln ( 2 )}]_{0}^{2}

Berechne die Grenzen:

\frac{1023}{5 ln ( 2 )}

= \frac{1023}{5 ln ( 2 )}

\int_{0}^{3} (2 x + 5) d x

\int_{0}^{1} cosh^{2} (x) d x

\int_{1}^{9} 3 u d u

\int_{0}^{0.34} ln (1 + x^{2}) d x

\int_{- 3}^{0} x (x + 3) (x + 1) d x