de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (8x^4-9x^3+6x^2-2x+1)/(x^2)

Lösung

\int \frac{8 x ^{4} - 9 x ^{3} + 6 x ^{2} - 2 x + 1}{x ^{2}} d x

Lösung

\frac{8 x ^{3}}{3} - \frac{9 x ^{2}}{2} + 6 x - 2 ln ∣ x ∣ - \frac{1}{x} + C

Schritte zur Lösung

\int \frac{8 x ^{4} - 9 x ^{3} + 6 x ^{2} - 2 x + 1}{x ^{2}} d x

Multipliziere aus

\frac{8 x ^{4} - 9 x ^{3} + 6 x ^{2} - 2 x + 1}{x ^{2}} : 8 x^{2} - 9 x + 6 - \frac{2}{x} + \frac{1}{x ^{2}}

= \int 8 x^{2} - 9 x + 6 - \frac{2}{x} + \frac{1}{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 8 x^{2} d x - \int 9 x d x + \int 6 d x - \int \frac{2}{x} d x + \int \frac{1}{x ^{2}} d x

\int 8 x^{2} d x = \frac{8 x ^{3}}{3}

\int 9 x d x = \frac{9 x ^{2}}{2}

\int 6 d x = 6 x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

= \frac{8 x ^{3}}{3} - \frac{9 x ^{2}}{2} + 6 x - 2 ln ∣ x ∣ - \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{8 x ^{3}}{3} - \frac{9 x ^{2}}{2} + 6 x - 2 ln ∣ x ∣ - \frac{1}{x} + C

Graph

Beliebte Beispiele

integral of (5x^2+2)^610

\int (5 x^{2} + 2)^{6} 10 d x

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

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

integral of 1/(\sqrt[5]{t^4)}

\int \frac{1}{5 t ^{4}} d t

integral of 4/(xsqrt(1+9x^2))

\int \frac{4}{x 1 + 9 x ^{2}} d x

integral of 1/(sqrt(14-x^2))

\int \frac{1}{14 - x ^{2}} d x