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^3-4+x))/(x-2)

Lösung

\int \frac{( x ^{3} - 4 + x )}{x - 2} d x

Lösung

3 x^{2} + x + 6 ln ∣ x - 2 ∣ + \frac{1}{3} (x - 2)^{3} - 14 + C

Schritte zur Lösung

\int \frac{x ^{3} - 4 + x}{x - 2} d x

Multipliziere aus

\frac{x ^{3} - 4 + x}{x - 2} : \frac{x ^{3}}{x - 2} - \frac{4}{x - 2} + \frac{x}{x - 2}

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{x ^{3}}{x - 2} d x - \int \frac{4}{x - 2} d x + \int \frac{x}{x - 2} d x

\int \frac{x ^{3}}{x - 2} d x = 3 x^{2} + 8 ln ∣ x - 2 ∣ + \frac{1}{3} (x - 2)^{3} - 12

\int \frac{4}{x - 2} d x = 4 ln ∣ x - 2 ∣

\int \frac{x}{x - 2} d x = x - 2 + 2 ln ∣ x - 2 ∣

= 3 x^{2} + 8 ln ∣ x - 2 ∣ + \frac{1}{3} (x - 2)^{3} - 12 - 4 ln ∣ x - 2 ∣ + x - 2 + 2 ln ∣ x - 2 ∣

Vereinfache

= 3 x^{2} + x + 6 ln ∣ x - 2 ∣ + \frac{1}{3} (x - 2)^{3} - 14

Füge eine Konstante zur Lösung hinzu

= 3 x^{2} + x + 6 ln ∣ x - 2 ∣ + \frac{1}{3} (x - 2)^{3} - 14 + C

Graph

Beliebte Beispiele

integral of (sqrt(x)+7)(x-sqrt(x)+1)

\int (x + 7) (x - x + 1) d x

integral of cos^4(6x)sin(6x)

\int cos^{4} (6 x) sin (6 x) d x

integral of sin^2(3u)

\int sin^{2} (3 u) d u

integral of (x^3+x^2+2)/((x^2+2)^2)

\int \frac{x ^{3} + x ^{2} + 2}{( x ^{2} + 2 ) ^{2}} d x

integral of 1/(-e^x)

\int \frac{1}{- e ^{x}} d x