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Beliebt Rechnen >

integral from 0 to 1 of (1+e^x)/(e^x)

Lösung

\int_{0}^{1} \frac{1 + e ^{x}}{e ^{x}} d x

Lösung

- \frac{1}{e} + 2

+1

Dezimale

1.63212 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{1 + e ^{x}}{e ^{x}} d x

Multipliziere aus

\frac{1 + e ^{x}}{e ^{x}} : \frac{1}{e ^{x}} + 1

= \int_{0}^{1} \frac{1}{e ^{x}} + 1 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} \frac{1}{e ^{x}} d x + \int_{0}^{1} 1 d x

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

\int_{0}^{1} 1 d x = 1

= - \frac{1}{e} + 1 + 1

Vereinfache

= - \frac{1}{e} + 2

Graph

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