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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

\int \frac{1}{5 ( x - 3 )} d x = \frac{1}{5} ln ∣ x - 3 ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

(\partial)/(\partial x)(-y/x)

\frac{\partial}{\partial x} (- \frac{y}{x})

tangent f(x)=((x))/(x-4)

t an g e n t f (x) = \frac{( x )}{x - 4}

(\partial)/(\partial x)(sin(x^2+5))

\frac{\partial}{\partial x} (sin (x^{2} + 5))

(8-r^2)dr=r^3sin(θ)dθ

(8 - r^{2}) d r = r^{3} sin (θ) d θ

integral from 0 to 1 of (x-6)/(x^2-6x+8)

\int_{0}^{1} \frac{x - 6}{x ^{2} - 6 x + 8} d x