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Beliebt Rechnen >

integral of ((x-3)^3)/(x^2-9)

Lösung

\int \frac{( x - 3 ) ^{3}}{x ^{2} - 9} d x

Lösung

\frac{x ^{2}}{2} - 9 x + 36 ln ∣ x + 3 ∣ + C

Schritte zur Lösung

\int \frac{( x - 3 ) ^{3}}{x ^{2} - 9} d x

Lange Division

\frac{( x - 3 ) ^{3}}{x ^{2} - 9} : x - 9 + \frac{36}{x + 3}

= \int x - 9 + \frac{36}{x + 3} 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 d x - \int 9 d x + \int \frac{36}{x + 3} d x

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

\int 9 d x = 9 x

\int \frac{36}{x + 3} d x = 36 ln ∣ x + 3 ∣

= \frac{x ^{2}}{2} - 9 x + 36 ln ∣ x + 3 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - 9 x + 36 ln ∣ x + 3 ∣ + C

Graph

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