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Beliebt Rechnen >

integral of (x^2+11x-30)/(x^3-5x^2+6x)

Lösung

\int \frac{x ^{2} + 11 x - 30}{x ^{3} - 5 x ^{2} + 6 x} d x

Lösung

- 5 ln ∣ x ∣ + 2 ln ∣ x - 2 ∣ + 4 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int \frac{x ^{2} + 11 x - 30}{x ^{3} - 5 x ^{2} + 6 x} d x

Ermittle den Partialbruch von

\frac{x ^{2} + 11 x - 30}{x ^{3} - 5 x ^{2} + 6 x} : - \frac{5}{x} + \frac{2}{x - 2} + \frac{4}{x - 3}

= \int - \frac{5}{x} + \frac{2}{x - 2} + \frac{4}{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{5}{x} d x + \int \frac{2}{x - 2} d x + \int \frac{4}{x - 3} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

\int \frac{4}{x - 3} d x = 4 ln ∣ x - 3 ∣

= - 5 ln ∣ x ∣ + 2 ln ∣ x - 2 ∣ + 4 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= - 5 ln ∣ x ∣ + 2 ln ∣ x - 2 ∣ + 4 ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

integral of x/((4x^2+1)^5)

\int \frac{x}{( 4 x ^{2} + 1 ) ^{5}} d x

integral of 5xsqrt(x^2+3)

\int 5 x x^{2} + 3 d x

integral of (cos(e^{-x}))/(e^x)

\int \frac{cos ( e ^{- x} )}{e ^{x}} d x

integral of e^{e^x}^{e^x}

\int e^{e^{x}} d e^{e^{x}}

integral of 1/(4+5cos^2(x))

\int \frac{1}{4 + 5 cos ^{2} ( x )} d x