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Beliebt Rechnen >

integral of 1/((x^2+10x+24))

Lösung

\int \frac{1}{( x ^{2} + 10 x + 24 )} d x

Lösung

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

Schritte zur Lösung

\int \frac{1}{x ^{2} + 10 x + 24} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} + 10 x + 24} : \frac{1}{2 ( x + 4 )} - \frac{1}{2 ( x + 6 )}

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

\int \frac{1}{2 ( x + 4 )} d x = \frac{1}{2} ln ∣ x + 4 ∣

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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