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Beliebt Rechnen >

integral of 1/(x^2+9x)

Lösung

\int \frac{1}{x ^{2} + 9 x} d x

Lösung

\frac{1}{9} ln ∣ x ∣ - \frac{1}{9} ln ∣ x + 9 ∣ + C

Schritte zur Lösung

\int \frac{1}{x ^{2} + 9 x} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} + 9 x} : \frac{1}{9 x} - \frac{1}{9 ( x + 9 )}

= \int \frac{1}{9 x} - \frac{1}{9 ( x + 9 )} 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}{9 x} d x - \int \frac{1}{9 ( x + 9 )} d x

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

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

= \frac{1}{9} ln ∣ x ∣ - \frac{1}{9} ln ∣ x + 9 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{9} ln ∣ x ∣ - \frac{1}{9} ln ∣ x + 9 ∣ + C

Graph

Beliebte Beispiele

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\int 8 x^{3} 2 x^{4} + 6 d x

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\int (\frac{x - 1}{x}) d x

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\int \frac{x ^{4} - x ^{2} - x - 1}{x ^{3} - x ^{2}} d x