integral from 0 to 1 of 2^x*3^x

Lösung

\int_{0}^{1} 2^{x} \cdot 3^{x} d x

\frac{5}{ln ( 6 )}

Dezimale

2.79055 \dots

Schritte zur Lösung

\int_{0}^{1} 2^{x} \cdot 3^{x} d x

Vereinfache

2^{x} \cdot 3^{x} : 6^{x}

= \int_{0}^{1} 6^{x} d x

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

= [\frac{6 ^{x}}{ln ( 6 )}]_{0}^{1}

Berechne die Grenzen:

\frac{5}{ln ( 6 )}

= \frac{5}{ln ( 6 )}

\int_{0}^{1} x 33 x^{2} + 16 d x

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

\int_{1}^{2} arctan (x) d x

\int_{0}^{0.8} 48000 x - 21600 d x

\int_{0}^{1} (3 x)^{2} - (3 x^{2})^{2} d x