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Beliebt Rechnen >

integral of (3x+1)/(x^2-x-6)

Lösung

\int \frac{3 x + 1}{x ^{2} - x - 6} d x

Lösung

ln ∣ x + 2 ∣ + 2 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int \frac{3 x + 1}{x ^{2} - x - 6} d x

Ermittle den Partialbruch von

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

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

\int \frac{1}{x + 2} d x = ln ∣ x + 2 ∣

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

= ln ∣ x + 2 ∣ + 2 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x + 2 ∣ + 2 ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

integral of e^{-3/5 x}

\int e^{- \frac{3}{5} x} d x

integral of 12x^5y^2

\int 12 x^{5} y^{2} d x

integral of 1/(xsqrt(1-2x^2))

\int \frac{1}{x 1 - 2 x ^{2}} d x

integral of+3x^5sqrt(x^3+1)

\int + 3 x^{5} x^{3} + 1 d x

integral of 1/(tan(x/5))

\int \frac{1}{tan ( \frac{x}{5} )} d x