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Beliebt Rechnen >

integral of (1+6x)/((4x-3)(2x+5))

Lösung

\int \frac{1 + 6 x}{( 4 x - 3 ) ( 2 x + 5 )} d x

Lösung

\frac{11}{52} ln ∣ 4 x - 3 ∣ + \frac{7}{13} ln ∣ 2 x + 5 ∣ + C

Schritte zur Lösung

\int \frac{1 + 6 x}{( 4 x - 3 ) ( 2 x + 5 )} d x

Ermittle den Partialbruch von

\frac{1 + 6 x}{( 4 x - 3 ) ( 2 x + 5 )} : \frac{11}{13 ( 4 x - 3 )} + \frac{14}{13 ( 2 x + 5 )}

= \int \frac{11}{13 ( 4 x - 3 )} + \frac{14}{13 ( 2 x + 5 )} 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{11}{13 ( 4 x - 3 )} d x + \int \frac{14}{13 ( 2 x + 5 )} d x

\int \frac{11}{13 ( 4 x - 3 )} d x = \frac{11}{52} ln ∣ 4 x - 3 ∣

\int \frac{14}{13 ( 2 x + 5 )} d x = \frac{7}{13} ln ∣ 2 x + 5 ∣

= \frac{11}{52} ln ∣ 4 x - 3 ∣ + \frac{7}{13} ln ∣ 2 x + 5 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{11}{52} ln ∣ 4 x - 3 ∣ + \frac{7}{13} ln ∣ 2 x + 5 ∣ + C

Graph

Beliebte Beispiele

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