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Beliebt Rechnen >

integral of (x+11)/((x-4)(x+1))

Lösung

\int \frac{x + 11}{( x - 4 ) ( x + 1 )} d x

Lösung

3 ln ∣ x - 4 ∣ - 2 ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int \frac{x + 11}{( x - 4 ) ( x + 1 )} d x

Ermittle den Partialbruch von

\frac{x + 11}{( x - 4 ) ( x + 1 )} : \frac{3}{x - 4} - \frac{2}{x + 1}

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

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

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

= 3 ln ∣ x - 4 ∣ - 2 ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= 3 ln ∣ x - 4 ∣ - 2 ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

derivative y=sqrt(ax+b)

d er i v a t i v e y = a x + b

fläche x^2=y,x^2=-(y-2)

a re a x^{2} = y, x^{2} = - (y - 2)

(\partial)/(\partial x)(x+3y^{1/3})

\frac{\partial}{\partial x} (x + 3 y^{\frac{1}{3}})

-y^'+(3y)/x =(y^2)/x

- y^{^{'}} + \frac{3 y}{x} = \frac{y ^{2}}{x}

derivative of (7x^2+3x+7/(sqrt(x)))

\frac{d}{d x} (\frac{7 x ^{2} + 3 x + 7}{x})