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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{5} ln ∣ x + 2 ∣ + \frac{4}{5} ln ∣ x - 3 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

= \int \frac{1}{5 ( x + 2 )} + \frac{4}{5 ( 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}{5 ( x + 2 )} d x + \int \frac{4}{5 ( x - 3 )} d x

\int \frac{1}{5 ( x + 2 )} d x = \frac{1}{5} ln ∣ x + 2 ∣

\int \frac{4}{5 ( x - 3 )} d x = \frac{4}{5} ln ∣ x - 3 ∣

= \frac{1}{5} ln ∣ x + 2 ∣ + \frac{4}{5} ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} ln ∣ x + 2 ∣ + \frac{4}{5} ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

derivative of (e^x+1^7)

\frac{d}{d x} ((e^{x} + 1)^{7})

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

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

(\partial)/(\partial y)(ye^{xy}-1/y)

\frac{\partial}{\partial y} (y e^{x y} - \frac{1}{y})

derivative of 4x^3-66x^2+216x

\frac{d}{d x} (4 x^{3} - 66 x^{2} + 216 x)

derivative of cos^2(x^3-ln(x^2-1))

\frac{d}{d x} (cos^{2} (x^{3}) - ln (x^{2} - 1))