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Beliebt Rechnen >

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

Lösung

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

Lösung

x - 4 ln ∣ x - 1 ∣ + 7 ln ∣ x - 2 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x ^{2} + 3}{x ^{2} - 3 x + 2} : 1 - \frac{4}{x - 1} + \frac{7}{x - 2}

= \int 1 - \frac{4}{x - 1} + \frac{7}{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 1 d x - \int \frac{4}{x - 1} d x + \int \frac{7}{x - 2} d x

\int 1 d x = x

\int \frac{4}{x - 1} d x = 4 ln ∣ x - 1 ∣

\int \frac{7}{x - 2} d x = 7 ln ∣ x - 2 ∣

= x - 4 ln ∣ x - 1 ∣ + 7 ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= x - 4 ln ∣ x - 1 ∣ + 7 ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

integral of (3x^2+cos(x))

\int (3 x^{2} + cos (x)) d x

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\frac{\partial}{\partial x} (\frac{x}{1 + x ^{2} y ^{2}})

integral of x(x+7)^6

\int x (x + 7)^{6} d x

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