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Beliebt Rechnen >

integral of (x+10)/(x^2+3x+2)

Lösung

\int \frac{x + 10}{x ^{2} + 3 x + 2} d x

Lösung

9 ln ∣ x + 1 ∣ - 8 ln ∣ x + 2 ∣ + C

Schritte zur Lösung

\int \frac{x + 10}{x ^{2} + 3 x + 2} d x

Ermittle den Partialbruch von

\frac{x + 10}{x ^{2} + 3 x + 2} : \frac{9}{x + 1} - \frac{8}{x + 2}

= \int \frac{9}{x + 1} - \frac{8}{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{9}{x + 1} d x - \int \frac{8}{x + 2} d x

\int \frac{9}{x + 1} d x = 9 ln ∣ x + 1 ∣

\int \frac{8}{x + 2} d x = 8 ln ∣ x + 2 ∣

= 9 ln ∣ x + 1 ∣ - 8 ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= 9 ln ∣ x + 1 ∣ - 8 ln ∣ x + 2 ∣ + C

Graph

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\int 2 cos (2 x) - 6 d x

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\int sin (2 x) + 1 d x