integral of (x^3-x^2+2x-6)/x

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

\int 2 d x = 2 x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

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

Füge eine Konstante zur Lösung hinzu

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

a re a 4 x + 7, 2 x + 29, 6, 16

x \to - 4 lim ((1 - x)^{3})

n = 1 \sum \infty (x + 5)^{n}

d er i v a t i v e y = (x^{4} + 1)^{4}

\int \frac{1}{x ^{2} + 11 x + 28} d x