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Beliebt Rechnen >

integral of (x^3-4x^2+5)/(x-4)

Lösung

\int \frac{x ^{3} - 4 x ^{2} + 5}{x - 4} d x

Lösung

\frac{x ^{3}}{3} + 5 ln ∣ x - 4 ∣ + C

Schritte zur Lösung

\int \frac{x ^{3} - 4 x ^{2} + 5}{x - 4} d x

Lange Division

\frac{x ^{3} - 4 x ^{2} + 5}{x - 4} : x^{2} + \frac{5}{x - 4}

= \int x^{2} + \frac{5}{x - 4} 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 \frac{5}{x - 4} d x

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

\int \frac{5}{x - 4} d x = 5 ln ∣ x - 4 ∣

= \frac{x ^{3}}{3} + 5 ln ∣ x - 4 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + 5 ln ∣ x - 4 ∣ + C

Graph

Beliebte Beispiele

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\int x e^{\frac{- x}{5}} d x

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