integral of xe^{1/x}

Lösung

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

x \to - 2 lim (\frac{x ^{2} - 4}{x + 2})

d er i v a t i v e e^{\frac{6}{x}}

x \to 3.01 lim (x^{2} + 3 x)

x \frac{d y}{d x} = 2 x e^{x^{2}} - y + 6 x^{2}

y^{^{'}} + y - 3 cos (x) = 0