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^2-3)/(x+1)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u ^{2} - 2 u - 2}{u} d u

Multipliziere aus

\frac{u ^{2} - 2 u - 2}{u} : u - 2 - \frac{2}{u}

= \int u - 2 - \frac{2}{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 u d u - \int 2 d u - \int \frac{2}{u} d u

\int u d u = \frac{u ^{2}}{2}

\int 2 d u = 2 u

\int \frac{2}{u} d u = 2 ln ∣ u ∣

= \frac{u ^{2}}{2} - 2 u - 2 ln ∣ u ∣

Setze in

u = x + 1

ein

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 1/(sqrt(4x^2+1))

\int \frac{1}{4 x ^{2} + 1} d x

limit as x approaches 1 of 3f(x)-2h(x)

x \to 1 lim (3 f (x) - 2 h (x))

derivative y=3^{cos(2x)}+e^3

d er i v a t i v e y = 3^{c o s (2 x)} + e^{3}

integral of 7sin(θ/3)

\int 7 sin (\frac{θ}{3}) d θ

(\partial)/(\partial y)(tan(x^2+y))

\frac{\partial}{\partial y} (tan (x^{2} + y))