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^4-6x^3+x-2)/(x-2)

Lösung

\int \frac{2 x ^{4} - 6 x ^{3} + x - 2}{x - 2} d x

Lösung

\frac{x ^{4}}{2} - \frac{2 x ^{3}}{3} - 2 x^{2} - 7 x - 16 ln ∣ x - 2 ∣ + C

Schritte zur Lösung

\int \frac{2 x ^{4} - 6 x ^{3} + x - 2}{x - 2} d x

Lange Division

\frac{2 x ^{4} - 6 x ^{3} + x - 2}{x - 2} : 2 x^{3} - 2 x^{2} - 4 x - 7 - \frac{16}{x - 2}

= \int 2 x^{3} - 2 x^{2} - 4 x - 7 - \frac{16}{x - 2} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x^{3} d x - \int 2 x^{2} d x - \int 4 x d x - \int 7 d x - \int \frac{16}{x - 2} d x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int 4 x d x = 2 x^{2}

\int 7 d x = 7 x

\int \frac{16}{x - 2} d x = 16 ln ∣ x - 2 ∣

= \frac{x ^{4}}{2} - \frac{2 x ^{3}}{3} - 2 x^{2} - 7 x - 16 ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{2} - \frac{2 x ^{3}}{3} - 2 x^{2} - 7 x - 16 ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

integral of 2sqrt(1-5x^2)

\int 2 1 - 5 x^{2} d x

integral of 1/(sqrt(2x^2+4x+3))

\int \frac{1}{2 x ^{2} + 4 x + 3} d x

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

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

integral of (2x^2+3)/(x^4-2x^2+1)

\int \frac{2 x ^{2} + 3}{x ^{4} - 2 x ^{2} + 1} d x

integral of (t^3)/(e^{2t^4)}

\int \frac{t ^{3}}{e ^{2 t^{4}}} d t