de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{4} ln ∣ x - 1 ∣ - \frac{1}{2 ( x - 1 )} - \frac{1}{4} ln ∣ x + 1 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x}{( 1 - x ) ^{2} ( 1 + x )} : \frac{1}{4 ( x - 1 )} + \frac{1}{2 ( x - 1 ) ^{2}} - \frac{1}{4 ( x + 1 )}

= \int \frac{1}{4 ( x - 1 )} + \frac{1}{2 ( x - 1 ) ^{2}} - \frac{1}{4 ( 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}{4 ( x - 1 )} d x + \int \frac{1}{2 ( x - 1 ) ^{2}} d x - \int \frac{1}{4 ( x + 1 )} d x

\int \frac{1}{4 ( x - 1 )} d x = \frac{1}{4} ln ∣ x - 1 ∣

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

\int \frac{1}{4 ( x + 1 )} d x = \frac{1}{4} ln ∣ x + 1 ∣

= \frac{1}{4} ln ∣ x - 1 ∣ - \frac{1}{2 ( x - 1 )} - \frac{1}{4} ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} ln ∣ x - 1 ∣ - \frac{1}{2 ( x - 1 )} - \frac{1}{4} ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

integral of (e^{3x})/(3-e^{3x)}

\int \frac{e ^{3 x}}{3 - e ^{3 x}} d x

integral of (e^x)/((2-e^x)^2)

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

integral of arcsin(2x+2)

\int arcsin (2 x + 2) d x

integral of 1/(1-cos^2(y))

\int \frac{1}{1 - cos ^{2} ( y )} d y

integral of 1/(x^2)+3

\int \frac{1}{x ^{2}} + 3 d x