integral of (e^{1/x}-x)/(x^2)

Lösung

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

- e^{\frac{1}{x}} - ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{e ^{\frac{1}{x}} - x}{x ^{2}} : \frac{e ^{\frac{1}{x}}}{x ^{2}} - \frac{1}{x}

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= - e^{\frac{1}{x}} - ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= - e^{\frac{1}{x}} - ln ∣ x ∣ + C

\int 6 x (x^{3} - 1)^{3} d x

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