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Beliebt Rechnen >

integral from 1 to 9 of e^{sqrt(x)}

Lösung

\int_{1}^{9} e^{x} d x

Lösung

4 e^{3}

+1

Dezimale

80.34214 \dots

Schritte zur Lösung

\int_{1}^{9} e^{x} d x

Wende U-Substitution an

= \int_{1}^{3} e^{u} \cdot 2 u d u

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{3} e^{u} u d u

Wende die partielle Integration an

= 2 [e^{u} u - \int e^{u} d u]_{1}^{3}

\int e^{u} d u = e^{u}

= 2 [e^{u} u - e^{u}]_{1}^{3}

Berechne die Grenzen:

2 e^{3}

= 2 \cdot 2 e^{3}

Vereinfache

= 4 e^{3}

Graph

Beliebte Beispiele

sum from k=1 to infinity of 1/(k^4)

k = 1 \sum \infty \frac{1}{k ^{4}}

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d er i v a t i v e 4 x^{2} cos (x) + 3 x

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\int 4 e^{x} sec (e^{x} + 2) d x

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\int \frac{( x - 1 )}{( x - 1 ) ^{2} + 1} d x

inverselaplace 1/(s^{3/2)}

in v erse l a pl a ce \frac{1}{s ^{\frac{3}{2}}}