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^2-3x+2)/(x+1)

Lösung

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

Lösung

\frac{( x + 1 ) ^{2}}{2} - 5 (x + 1) + 6 ln ∣ x + 1 ∣ + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{u ^{2} - 5 u + 6}{u} d u

Multipliziere aus

\frac{u ^{2} - 5 u + 6}{u} : u - 5 + \frac{6}{u}

= \int u - 5 + \frac{6}{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 5 d u + \int \frac{6}{u} d u

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

\int 5 d u = 5 u

\int \frac{6}{u} d u = 6 ln ∣ u ∣

= \frac{u ^{2}}{2} - 5 u + 6 ln ∣ u ∣

Setze in

u = x + 1

ein

= \frac{( x + 1 ) ^{2}}{2} - 5 (x + 1) + 6 ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{( x + 1 ) ^{2}}{2} - 5 (x + 1) + 6 ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

integral of (5y^4)/(y^5-13)

\int \frac{5 y ^{4}}{y ^{5} - 13} d y

inverselaplace (50s)/(s^2+25)

in v erse l a pl a ce \frac{50 s}{s ^{2} + 25}

(\partial)/(\partial x)(e^{-x}y)

\frac{\partial}{\partial x} (e^{- x} y)

integral from-2 to 5 of |-x^3+9x|

\int_{- 2}^{5} - x^{3} + 9 x d x

derivative of 4cot(x)

\frac{d}{d x} (4 cot (x))