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Beliebt Rechnen >

integral of x/(x^2+3x+2)

Lösung

\int \frac{x}{x ^{2} + 3 x + 2} d x

Lösung

- ln ∣ x + 1 ∣ + 2 ln ∣ x + 2 ∣ + C

Schritte zur Lösung

\int \frac{x}{x ^{2} + 3 x + 2} d x

Ermittle den Partialbruch von

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

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

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

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

= - ln ∣ x + 1 ∣ + 2 ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= - ln ∣ x + 1 ∣ + 2 ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

derivative of arctan(ax^2)

\frac{d}{d x} (arctan (a x^{2}))

implicit (dy)/(dx),y^2=x^3

im pl i c i t \frac{d y}{d x}, y^{2} = x^{3}

derivative of 6ln(x)

\frac{d}{d x} (6 ln (x))

derivative y=(x^7-2x^4+14x)/(x^4)

d er i v a t i v e y = \frac{x ^{7} - 2 x ^{4} + 14 x}{x ^{4}}

limit as x approaches 3 of ((x^2))/(x-3)

x \to 3 lim (\frac{( x ^{2} )}{x - 3})