de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of 1/(e^t+1)

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

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

\int 1 d t = t

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (ln(x))^{12} 1/x

\int (ln (x))^{12} \frac{1}{x} d x

integral of (tcos(t))

\int (t cos (t)) d t

integral of (ln^9(z))/z

\int \frac{ln ^{9} ( z )}{z} d z

integral of te^{-kt}

\int t e^{- k t} d t

integral of (3x)/((x-1)(x+2))

\int \frac{3 x}{( x - 1 ) ( x + 2 )} d x