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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

(\partial)/(\partial x)(5^{x^2})

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

integral of 4/(e^x)

\int \frac{4}{e ^{x}} d x

integral of e^{-11x}

\int e^{- 11 x} d x

inverselaplace (s+1)/(s^2+s+10)

in v erse l a pl a ce \frac{s + 1}{s ^{2} + s + 10}

derivative (sin(x))/(2x)

d er i v a t i v e \frac{sin ( x )}{2 x}