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Beliebt Rechnen >

integral of (3x-5)/(x^2-4x+3)

Lösung

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

Lösung

ln ∣ x - 1 ∣ + 2 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{3 x - 5}{x ^{2} - 4 x + 3} : \frac{1}{x - 1} + \frac{2}{x - 3}

= \int \frac{1}{x - 1} + \frac{2}{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{2}{x - 3} d x

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

\int \frac{2}{x - 3} d x = 2 ln ∣ x - 3 ∣

= ln ∣ x - 1 ∣ + 2 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x - 1 ∣ + 2 ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

integral of x^3+2x^2-x+k

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

limit as (x,y) approaches (2,1) of (x-2y)/(x^3-8y^3)

(x, y) \to (2, 1) lim (\frac{x - 2 y}{x ^{3} - 8 y ^{3}})

integral of 1/(u(u+2))

\int \frac{1}{u ( u + 2 )} d u

integral of 2x^2cos(5x)

\int 2 x^{2} cos (5 x) d x

integral of (4x^2+x+27)/(x^3+9x)

\int \frac{4 x ^{2} + x + 27}{x ^{3} + 9 x} d x