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Beliebt Rechnen >

integral of (10x+6)/(x^2-2x-3)

Lösung

\int \frac{10 x + 6}{x ^{2} - 2 x - 3} d x

Lösung

ln ∣ x + 1 ∣ + 9 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int \frac{10 x + 6}{x ^{2} - 2 x - 3} d x

Ermittle den Partialbruch von

\frac{10 x + 6}{x ^{2} - 2 x - 3} : \frac{1}{x + 1} + \frac{9}{x - 3}

= \int \frac{1}{x + 1} + \frac{9}{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{1}{x + 1} d x + \int \frac{9}{x - 3} d x

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

\int \frac{9}{x - 3} d x = 9 ln ∣ x - 3 ∣

= ln ∣ x + 1 ∣ + 9 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 1 ∣ + 9 ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

integral of 2/(100+2t)

\int \frac{2}{100 + 2 t} d t

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\int \frac{7 x}{( 6 - x ^{2} ) ^{3}} d x

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\int 3 sin (x) e^{x} d x

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\int \frac{5 - 2 y}{y ( y - 1 ) ^{2}} d y

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\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{8}} d x