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Beliebt Rechnen >

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

Lösung

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

Lösung

2 ln ∣ x + 1 ∣ + 3 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

= 2 ln ∣ x + 1 ∣ + 3 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x + 1 ∣ + 3 ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

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

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

derivative of sin(cos(4x))

\frac{d}{d x} (sin (cos (4 x)))

derivative 1/(5x^{4/5)}

d er i v a t i v e \frac{1}{5 x ^{\frac{4}{5}}}

derivative f(x)=(x^3+1)/(x^3-1)

d er i v a t i v e f (x) = \frac{x ^{3} + 1}{x ^{3} - 1}

x^3y^{'''}+xy^'-y=0

x^{3} y^{^{'''}} + x y^{^{'}} - y = 0