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Beliebt Rechnen >

integral from 1 to 2 of 18x^24^{x^3}

Lösung

\int_{1}^{2} 18 x^{2} 4^{x^{3}} d x

Lösung

\frac{196596}{ln ( 2 )}

+1

Dezimale

283628.07425 \dots

Schritte zur Lösung

\int_{1}^{2} 18 x^{2} \cdot 4^{x^{3}} d x

Entferne die Konstante:

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

= 18 \cdot \int_{1}^{2} x^{2} \cdot 4^{x^{3}} d x

Wende U-Substitution an

= 18 \cdot \int_{4}^{65536} \frac{u}{3 ln ( 2 ) \cdot 2 ^{\frac{l n ( u ) + l n ( 2 )}{l n ( 2 )}}} d u

Entferne die Konstante:

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

= 18 \cdot \frac{1}{3 ln ( 2 )} \cdot \int_{4}^{65536} \frac{u}{2 ^{\frac{l n ( u ) + l n ( 2 )}{l n ( 2 )}}} d u

Wende die partielle Integration an

= 18 \cdot \frac{1}{3 ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} - \int - \frac{1}{4} d u]_{4}^{65536}

\int - \frac{1}{4} d u = - \frac{1}{4} u

= 18 \cdot \frac{1}{3 ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} - (- \frac{1}{4} u)]_{4}^{65536}

Vereinfache

18 \cdot \frac{1}{3 ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} - (- \frac{1}{4} u)]_{4}^{65536} : \frac{6}{ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} + \frac{1}{4} u]_{4}^{65536}

= \frac{6}{ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} + \frac{1}{4} u]_{4}^{65536}

Berechne die Grenzen:

32766

= \frac{6}{ln ( 2 )} \cdot 32766

Vereinfache

= \frac{196596}{ln ( 2 )}

Graph

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