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Beliebt Rechnen >

integral of (3x^2-6x-4)/(x^3-3x^2-4x+12)

Lösung

\int \frac{3 x ^{2} - 6 x - 4}{x ^{3} - 3 x ^{2} - 4 x + 12} d x

Lösung

ln x^{3} - 3 x^{2} - 4 x + 12 + C

Schritte zur Lösung

\int \frac{3 x ^{2} - 6 x - 4}{x ^{3} - 3 x ^{2} - 4 x + 12} d x

Wende U-Substitution an

= \int \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Setze in

u = x^{3} - 3 x^{2} - 4 x + 12

ein

= ln x^{3} - 3 x^{2} - 4 x + 12

Füge eine Konstante zur Lösung hinzu

= ln x^{3} - 3 x^{2} - 4 x + 12 + C

Graph

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x \to 2 + lim (\frac{x ^{3} - 8}{x - 2})

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\int arccot (11 y) d y

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