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Beliebt Rechnen >

integral of (x+4)/((x+1)(x-2))

Lösung

\int \frac{x + 4}{( x + 1 ) ( x - 2 )} d x

Lösung

- ln ∣ x + 1 ∣ + 2 ln ∣ x - 2 ∣ + C

Schritte zur Lösung

\int \frac{x + 4}{( x + 1 ) ( x - 2 )} d x

Ermittle den Partialbruch von

\frac{x + 4}{( x + 1 ) ( 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

integral of e^{-e^{-x}}^{-e^{-x}}

\int e^{- e^{- x}} d e^{- e^{- x}}

integral of (3x^2e^{x^3-1})

\int (3 x^{2} e^{x^{3} - 1}) d x

integral of x(3x-2)^{1/3}

\int x (3 x - 2)^{\frac{1}{3}} d x

integral of 1/(cos^2(x)+1)

\int \frac{1}{cos ^{2} ( x ) + 1} d x

integral of ((4+x))/(1+x^2)

\int \frac{( 4 + x )}{1 + x ^{2}} d x