de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (2x^3+x^2-5)/(x-1)

Lösung

\int \frac{2 x ^{3} + x ^{2} - 5}{x - 1} d x

Lösung

3 x^{2} + 2 x + \frac{2}{3} (x - 1)^{3} + \frac{1}{2} (x - 1)^{2} - 2 ln ∣ x - 1 ∣ - 5 + C

Schritte zur Lösung

\int \frac{2 x ^{3} + x ^{2} - 5}{x - 1} d x

Multipliziere aus

\frac{2 x ^{3} + x ^{2} - 5}{x - 1} : \frac{2 x ^{3}}{x - 1} + \frac{x ^{2}}{x - 1} - \frac{5}{x - 1}

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{2 x ^{3}}{x - 1} d x + \int \frac{x ^{2}}{x - 1} d x - \int \frac{5}{x - 1} d x

\int \frac{2 x ^{3}}{x - 1} d x = 3 x^{2} + 2 ln ∣ x - 1 ∣ + \frac{2}{3} (x - 1)^{3} - 3

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

\int \frac{5}{x - 1} d x = 5 ln ∣ x - 1 ∣

= 3 x^{2} + 2 ln ∣ x - 1 ∣ + \frac{2}{3} (x - 1)^{3} - 3 + \frac{( x - 1 ) ^{2}}{2} + 2 (x - 1) + ln ∣ x - 1 ∣ - 5 ln ∣ x - 1 ∣

Vereinfache

3 x^{2} + 2 ln ∣ x - 1 ∣ + \frac{2}{3} (x - 1)^{3} - 3 + \frac{( x - 1 ) ^{2}}{2} + 2 (x - 1) + ln ∣ x - 1 ∣ - 5 ln ∣ x - 1 ∣ : 3 x^{2} + 2 x + \frac{2}{3} (x - 1)^{3} + \frac{1}{2} (x - 1)^{2} - 2 ln ∣ x - 1 ∣ - 5

= 3 x^{2} + 2 x + \frac{2}{3} (x - 1)^{3} + \frac{1}{2} (x - 1)^{2} - 2 ln ∣ x - 1 ∣ - 5

Füge eine Konstante zur Lösung hinzu

= 3 x^{2} + 2 x + \frac{2}{3} (x - 1)^{3} + \frac{1}{2} (x - 1)^{2} - 2 ln ∣ x - 1 ∣ - 5 + C

Graph

Beliebte Beispiele

(x^2+1)y^'+5x(y-1)=0,y(0)=9

(x^{2} + 1) y^{^{'}} + 5 x (y - 1) = 0, y (0) = 9

sum from n=0 to infinity of q^n

n = 0 \sum \infty q^{n}

integral of (1+8v)/(-16v^2)

\int \frac{1 + 8 v}{- 16 v ^{2}} d v

x(dy)/(dx)=x^2+3y

x \frac{d y}{d x} = x^{2} + 3 y

integral of ((x-2))/(sqrt(4x-x^2))

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