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Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x + 1 ∣ + 4 ln ∣ x + 2 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{5 x + 6}{x ^{2} + 3 x + 2} : \frac{1}{x + 1} + \frac{4}{x + 2}

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

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

\int \frac{4}{x + 2} d x = 4 ln ∣ x + 2 ∣

= ln ∣ x + 1 ∣ + 4 ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 1 ∣ + 4 ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

integral of x^6sin(x^7+8)

\int x^{6} sin (x^{7} + 8) d x

integral of 4/(5+6x)

\int \frac{4}{5 + 6 x} d x

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

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

integral of (x^3+4)/(x(x+1))

\int \frac{x ^{3} + 4}{x ( x + 1 )} d x

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

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