integral from 0 to ln(3) of 1/(1+e^x)

Lösung

\int_{0}^{l n (3)} \frac{1}{1 + e ^{x}} d x

- ln (2) + ln (3)

Dezimale

0.40546 \dots

Schritte zur Lösung

\int_{0}^{l n (3)} \frac{1}{1 + e ^{x}} d x

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

= \int_{0}^{l n (3)} - \frac{e ^{x}}{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}^{l n (3)} \frac{e ^{x}}{1 + e ^{x}} d x + \int_{0}^{l n (3)} 1 d x

\int_{0}^{l n (3)} \frac{e ^{x}}{1 + e ^{x}} d x = ln (2)

\int_{0}^{l n (3)} 1 d x = ln (3)

= - ln (2) + ln (3)

\int_{0}^{3} - e^{- 2 y} + 1 d y

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