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

Lösung

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

Lösung

x - 1 + ln ∣ x - 1 ∣ + C

Schritte zur Lösung

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

Vereinfache

\frac{x ^{2} + x}{x ^{2} - 1} : \frac{x}{x - 1}

= \int \frac{x}{x - 1} d x

Wende U-Substitution an

= \int \frac{u + 1}{u} d u

Multipliziere aus

\frac{u + 1}{u} : 1 + \frac{1}{u}

= \int 1 + \frac{1}{u} 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

= \int 1 d u + \int \frac{1}{u} d u

\int 1 d u = u

\int \frac{1}{u} d u = ln ∣ u ∣

= u + ln ∣ u ∣

Setze in

u = x - 1

ein

= x - 1 + ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= x - 1 + ln ∣ x - 1 ∣ + C

Graph

Beliebte Beispiele

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

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

integral of 1/(x^{3/4)-x^{1/4}}

\int \frac{1}{x ^{\frac{3}{4}} - x ^{\frac{1}{4}}} d x

integral of (18x^5-12x^3+4x)

\int (18 x^{5} - 12 x^{3} + 4 x) d x

integral of 7/(w^2+3w+3)

\int \frac{7}{w ^{2} + 3 w + 3} d w

integral of 4cot^3(x)csc(x)

\int 4 cot^{3} (x) csc (x) d x