integral from 0 to 9 of (e^{1/x})/(x^2)

Lösung

\int_{0}^{9} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

divergiert

Schritte zur Lösung

\int_{0}^{9} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

Wende die partielle Integration an

= [\frac{e ^{\frac{1}{x}}}{x} - \int \frac{- e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x}{x ^{3}} d x]_{0}^{9}

\int \frac{- e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x}{x ^{3}} d x = \frac{e ^{\frac{1}{x}}}{x} + e^{\frac{1}{x}}

= [\frac{e ^{\frac{1}{x}}}{x} - (\frac{e ^{\frac{1}{x}}}{x} + e^{\frac{1}{x}})]_{0}^{9}

Vereinfache

= [- e^{\frac{1}{x}}]_{0}^{9}

Berechne die Grenzen:

divergiert

= divergiert

\int_{1}^{9} (\frac{2}{x}) d x

\int_{π}^{x} cos (2 x) d x

\int_{0}^{\frac{π}{4}} x^{2} cos (x) d x

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\int_{0}^{1} e^{- x} - e^{x} d x