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Beliebt Rechnen >

integral of ((x+2))/((x-5)(x+3))

Lösung

\int \frac{( x + 2 )}{( x - 5 ) ( x + 3 )} d x

Lösung

\frac{7}{8} ln ∣ x - 5 ∣ + \frac{1}{8} ln ∣ x + 3 ∣ + C

Schritte zur Lösung

\int \frac{x + 2}{( x - 5 ) ( x + 3 )} d x

Ermittle den Partialbruch von

\frac{x + 2}{( x - 5 ) ( x + 3 )} : \frac{7}{8 ( x - 5 )} + \frac{1}{8 ( x + 3 )}

= \int \frac{7}{8 ( x - 5 )} + \frac{1}{8 ( 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 \frac{7}{8 ( x - 5 )} d x + \int \frac{1}{8 ( x + 3 )} d x

\int \frac{7}{8 ( x - 5 )} d x = \frac{7}{8} ln ∣ x - 5 ∣

\int \frac{1}{8 ( x + 3 )} d x = \frac{1}{8} ln ∣ x + 3 ∣

= \frac{7}{8} ln ∣ x - 5 ∣ + \frac{1}{8} ln ∣ x + 3 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{7}{8} ln ∣ x - 5 ∣ + \frac{1}{8} ln ∣ x + 3 ∣ + C

Graph

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