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Beliebt Rechnen >

integral of 1/(1+e^t)

Lösung

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

Lösung

- ln 1 + e^{t} + t + C

Schritte zur Lösung

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

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

= \int - \frac{e ^{t}}{1 + e ^{t}} + 1 d t

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{e ^{t}}{1 + e ^{t}} d t + \int 1 d t

\int \frac{e ^{t}}{1 + e ^{t}} d t = ln 1 + e^{t}

\int 1 d t = t

= - ln 1 + e^{t} + t

Füge eine Konstante zur Lösung hinzu

= - ln 1 + e^{t} + t + C

Graph

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