de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (28)/(28+e^x)

Lösung

\int \frac{28}{28 + e ^{x}} d x

Lösung

x - ln ∣ e^{x} + 28 ∣ + C

Schritte zur Lösung

\int \frac{28}{28 + e ^{x}} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 28 \cdot \int \frac{1}{28 + e ^{x}} d x

Wende U-Substitution an

= 28 \cdot \int \frac{1}{u ( 28 + u )} d u

Ermittle den Partialbruch von

\frac{1}{u ( 28 + u )} : \frac{1}{28 u} - \frac{1}{28 ( u + 28 )}

= 28 \cdot \int \frac{1}{28 u} - \frac{1}{28 ( u + 28 )} d u

Wende die Summenregel an:

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

= 28 (\int \frac{1}{28 u} d u - \int \frac{1}{28 ( u + 28 )} d u)

\int \frac{1}{28 u} d u = \frac{1}{28} ln ∣ u ∣

\int \frac{1}{28 ( u + 28 )} d u = \frac{1}{28} ln ∣ u + 28 ∣

= 28 (\frac{1}{28} ln ∣ u ∣ - \frac{1}{28} ln ∣ u + 28 ∣)

Setze in

u = e^{x}

ein

= 28 (\frac{1}{28} ln ∣ e^{x} ∣ - \frac{1}{28} ln ∣ e^{x} + 28 ∣)

Vereinfache

28 (\frac{1}{28} ln ∣ e^{x} ∣ - \frac{1}{28} ln ∣ e^{x} + 28 ∣) : x - ln ∣ e^{x} + 28 ∣

= x - ln ∣ e^{x} + 28 ∣

Füge eine Konstante zur Lösung hinzu

= x - ln ∣ e^{x} + 28 ∣ + C

Graph

Beliebte Beispiele

limit as x approaches 3+of 6+x

x \to 3 + lim (6 + x)

tangent y= 6/(x^2),(1,6)

t an g e n t y = \frac{6}{x ^{2}}, (1, 6)

integral of 1/(x^2(x^2-9))

\int \frac{1}{x ^{2} ( x ^{2} - 9 )} d x

tangent y=3x^3-x^2+5,(2,25)

t an g e n t y = 3 x^{3} - x^{2} + 5, (2, 25)

integral from 1 to infinity of 1/(x^4)

\int_{1}^{\infty} \frac{1}{x ^{4}} d x