integral from 1 to 2 of (e^x)/(x^2)

Lösung

\int_{1}^{2} \frac{e ^{x}}{x ^{2}} d x

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

Schritte zur Lösung

\int_{1}^{2} \frac{e ^{x}}{x ^{2}} d x

Wende die partielle Integration an

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

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

= [- \frac{e ^{x}}{x} - (- Ei (x))]_{1}^{2}

Vereinfache

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

Berechne die Grenzen:

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

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

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