integral from-7 to 0 of (e^{1/x})/(x^2)

Lösung

\int_{- 7}^{0} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

\frac{1}{e ^{\frac{1}{7}}}

Dezimale

0.86687 \dots

Schritte zur Lösung

\int_{- 7}^{0} \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]_{- 7}^{0}

\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}})]_{- 7}^{0}

Vereinfache

= [- e^{\frac{1}{x}}]_{- 7}^{0}

Berechne die Grenzen:

\frac{1}{e ^{\frac{1}{7}}}

= \frac{1}{e ^{\frac{1}{7}}}

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

\int_{0}^{π} cos^{2} (x) d x

\int_{0}^{5} \frac{1}{50} x d x

\int_{0.2}^{2} x d x

\int_{1}^{\infty} x e^{- 13 x} d x