integral e^{1/x}x

Lösung

integral

e^{\frac{1}{x}} x

\frac{1}{2} e^{\frac{1}{x}} x^{2} - \frac{1}{2} (- e^{\frac{1}{x}} x + Ei (\frac{1}{x})) + C

Schritte zur Lösung

\int e^{\frac{1}{x}} x d x

Wende die partielle Integration an

= \frac{1}{2} e^{\frac{1}{x}} x^{2} - \int - \frac{1}{2} e^{\frac{1}{x}} d x

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

= \frac{1}{2} e^{\frac{1}{x}} x^{2} - \frac{1}{2} (- e^{\frac{1}{x}} x + Ei (\frac{1}{x}))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} e^{\frac{1}{x}} x^{2} - \frac{1}{2} (- e^{\frac{1}{x}} x + Ei (\frac{1}{x})) + C

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