integral from-infinity to 15 of xe^{x/5}

Lösung

\int_{- \infty}^{15} x e^{\frac{x}{5}} d x

50 e^{3}

Dezimale

1004.27684 \dots

Schritte zur Lösung

\int_{- \infty}^{15} x e^{\frac{x}{5}} d x

Berechne das unbestimmte Integral:

\int x e^{\frac{x}{5}} d x = 5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}} + C

Berechne die Grenzen:

\int_{- \infty}^{15} x e^{\frac{x}{5}} d x = 50 e^{3} - 0

= 50 e^{3} - 0

Vereinfache

= 50 e^{3}

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

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