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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{x ^{3}}{12} - \frac{x ^{2}}{16} - \frac{9}{16} x - \frac{9}{32} ln ∣ 4 x - 2 ∣ + C

Schritte zur Lösung

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

Lange Division

\frac{x ^{3} - x ^{2} - 2 x}{4 x - 2} : \frac{x ^{2}}{4} - \frac{x}{8} - \frac{9}{16} - \frac{9}{8 ( 4 x - 2 )}

= \int \frac{x ^{2}}{4} - \frac{x}{8} - \frac{9}{16} - \frac{9}{8 ( 4 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 \frac{x ^{2}}{4} d x - \int \frac{x}{8} d x - \int \frac{9}{16} d x - \int \frac{9}{8 ( 4 x - 2 )} d x

\int \frac{x ^{2}}{4} d x = \frac{x ^{3}}{12}

\int \frac{x}{8} d x = \frac{x ^{2}}{16}

\int \frac{9}{16} d x = \frac{9}{16} x

\int \frac{9}{8 ( 4 x - 2 )} d x = \frac{9}{32} ln ∣ 4 x - 2 ∣

= \frac{x ^{3}}{12} - \frac{x ^{2}}{16} - \frac{9}{16} x - \frac{9}{32} ln ∣ 4 x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{12} - \frac{x ^{2}}{16} - \frac{9}{16} x - \frac{9}{32} ln ∣ 4 x - 2 ∣ + C

Graph

Beliebte Beispiele

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