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

Lösung

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

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

Schritte zur Lösung

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

Lange Division

\frac{x ^{3} - 1}{x - 2} : x^{2} + 2 x + 4 + \frac{7}{x - 2}

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

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

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

\int 4 d x = 4 x

\int \frac{7}{x - 2} d x = 7 ln ∣ x - 2 ∣

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e x^{7} (x - 10)^{3}

\int ((2 x - 1) y^{2} sin (4 x y)) d x

\int 17 x e^{19 x} d x

x \to 0 + lim ((tan (5 x))^{x})

\frac{d}{d x} (- \frac{e ^{x}}{x})