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Beliebt Rechnen >

integral of (e^{6/x})/(x^2)

Lösung

\int \frac{e ^{\frac{6}{x}}}{x ^{2}} d x

Lösung

- \frac{1}{6} e^{\frac{6}{x}} + C

Schritte zur Lösung

\int \frac{e ^{\frac{6}{x}}}{x ^{2}} d x

Wende U-Substitution an

= \int - \frac{e ^{u}}{6} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{6} \cdot \int e^{u} d u

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= - \frac{1}{6} e^{u}

Setze in

u = \frac{6}{x}

ein

= - \frac{1}{6} e^{\frac{6}{x}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{6} e^{\frac{6}{x}} + C

Graph

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