integral from 0 to 1 of xe^{x/a}

Lösung

\int_{0}^{1} x e^{\frac{x}{a}} d x

a e^{\frac{1}{a}} - a^{2} e^{\frac{1}{a}} + a^{2}

Schritte zur Lösung

\int_{0}^{1} x e^{\frac{x}{a}} d x

Wende die partielle Integration an

= [a e^{\frac{x}{a}} x - \int a e^{\frac{x}{a}} d x]_{0}^{1}

\int a e^{\frac{x}{a}} d x = a^{2} e^{\frac{x}{a}}

= [a e^{\frac{x}{a}} x - a^{2} e^{\frac{x}{a}}]_{0}^{1}

Berechne die Grenzen:

a e^{\frac{1}{a}} - a^{2} e^{\frac{1}{a}} + a^{2}

= a e^{\frac{1}{a}} - a^{2} e^{\frac{1}{a}} + a^{2}

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