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Beliebt Rechnen >

integral of 1/((x-4)(x+2))

Lösung

\int \frac{1}{( x - 4 ) ( x + 2 )} d x

Lösung

\frac{1}{6} ln ∣ x - 4 ∣ - \frac{1}{6} ln ∣ x + 2 ∣ + C

Schritte zur Lösung

\int \frac{1}{( x - 4 ) ( x + 2 )} d x

Ermittle den Partialbruch von

\frac{1}{( x - 4 ) ( x + 2 )} : \frac{1}{6 ( x - 4 )} - \frac{1}{6 ( x + 2 )}

= \int \frac{1}{6 ( x - 4 )} - \frac{1}{6 ( 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{1}{6 ( x - 4 )} d x - \int \frac{1}{6 ( x + 2 )} d x

\int \frac{1}{6 ( x - 4 )} d x = \frac{1}{6} ln ∣ x - 4 ∣

\int \frac{1}{6 ( x + 2 )} d x = \frac{1}{6} ln ∣ x + 2 ∣

= \frac{1}{6} ln ∣ x - 4 ∣ - \frac{1}{6} ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{6} ln ∣ x - 4 ∣ - \frac{1}{6} ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

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

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\int (cos^{7} (y) sin^{2} (y)) d y

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