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Beliebt Rechnen >

integral from-1 to 1 of e^{u+1}

Lösung

\int_{- 1}^{1} e^{u + 1} d u

Lösung

e^{2} - 1

+1

Dezimale

6.38905 \dots

Schritte zur Lösung

\int_{- 1}^{1} e^{u + 1} d u

e^{u + 1} = e^{1} e^{u}

= \int_{- 1}^{1} e^{1} e^{u} d u

Entferne die Konstante:

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

= e^{1} \cdot \int_{- 1}^{1} e^{u} d u

Vereinfache

= e \cdot \int_{- 1}^{1} e^{u} d u

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

e - \frac{1}{e}

= e (e - \frac{1}{e})

Vereinfache

= e^{2} - 1

Graph

Beliebte Beispiele

limit as x approaches 2 of (x^2+1)/(x-2)

x \to 2 lim (\frac{x ^{2} + 1}{x - 2})

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derivative y=ln(x/(1+x^2))

d er i v a t i v e y = ln (\frac{x}{1 + x ^{2}})

4/10 x^2dy-13dx=0

\frac{4}{10} x^{2} d y - 13 d x = 0

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in v erse l a pl a ce \frac{3}{( s - 2 ) ^{2}}