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Beliebt Rechnen >

integral of ((1+e^x))/(e^x)

Lösung

\int \frac{( 1 + e ^{x} )}{e ^{x}} d x

Lösung

- \frac{1}{e ^{x}} + x + C

Schritte zur Lösung

\int \frac{1 + e ^{x}}{e ^{x}} d x

Multipliziere aus

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

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

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

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{e ^{x}} + x + C

Graph

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