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Beliebt Rechnen >

integral of ((x+2)^2)/(x-2)

Lösung

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

Lösung

\frac{x ^{2}}{2} + 6 x + 16 ln ∣ x - 2 ∣ + C

Schritte zur Lösung

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

Lange Division

\frac{( x + 2 ) ^{2}}{x - 2} : x + 6 + \frac{16}{x - 2}

= \int x + 6 + \frac{16}{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 d x + \int 6 d x + \int \frac{16}{x - 2} d x

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

\int 6 d x = 6 x

\int \frac{16}{x - 2} d x = 16 ln ∣ x - 2 ∣

= \frac{x ^{2}}{2} + 6 x + 16 ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + 6 x + 16 ln ∣ x - 2 ∣ + C

Graph

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