integral from 1 to 2 of (e^{3x})/(x^2)

Lösung

\int_{1}^{2} \frac{e ^{3 x}}{x ^{2}} d x

- \frac{e ^{6}}{2} + 3 Ei (3 \cdot 2) + e^{3} - 3 Ei (3 \cdot 1)

Schritte zur Lösung

\int_{1}^{2} \frac{e ^{3 x}}{x ^{2}} d x

Wende die partielle Integration an

= [- \frac{e ^{3 x}}{x} - \int - \frac{3 e ^{3 x}}{x} d x]_{1}^{2}

\int - \frac{3 e ^{3 x}}{x} d x = - 3 Ei (3 x)

= [- \frac{e ^{3 x}}{x} - (- 3 Ei (3 x))]_{1}^{2}

Vereinfache

= [- \frac{e ^{3 x}}{x} + 3 Ei (3 x)]_{1}^{2}

Berechne die Grenzen:

- \frac{e ^{6}}{2} + 3 Ei (3 \cdot 2) + e^{3} - 3 Ei (3 \cdot 1)

= - \frac{e ^{6}}{2} + 3 Ei (3 \cdot 2) + e^{3} - 3 Ei (3 \cdot 1)

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