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Beliebt Rechnen >

integral of (3x+2)/((x-4)(x+2))

Lösung

\int \frac{3 x + 2}{( x - 4 ) ( x + 2 )} d x

Lösung

\frac{7}{3} ln ∣ x - 4 ∣ + \frac{2}{3} ln ∣ x + 2 ∣ + C

Schritte zur Lösung

\int \frac{3 x + 2}{( x - 4 ) ( x + 2 )} d x

Ermittle den Partialbruch von

\frac{3 x + 2}{( x - 4 ) ( x + 2 )} : \frac{7}{3 ( x - 4 )} + \frac{2}{3 ( x + 2 )}

= \int \frac{7}{3 ( x - 4 )} + \frac{2}{3 ( 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{7}{3 ( x - 4 )} d x + \int \frac{2}{3 ( x + 2 )} d x

\int \frac{7}{3 ( x - 4 )} d x = \frac{7}{3} ln ∣ x - 4 ∣

\int \frac{2}{3 ( x + 2 )} d x = \frac{2}{3} ln ∣ x + 2 ∣

= \frac{7}{3} ln ∣ x - 4 ∣ + \frac{2}{3} ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{7}{3} ln ∣ x - 4 ∣ + \frac{2}{3} ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

integral of (5x+1)(2x-2)

\int (5 x + 1) (2 x - 2) d x

integral of (2x^2-5x-7)/(x-3)

\int \frac{2 x ^{2} - 5 x - 7}{x - 3} d x

integral of (6x)/(e^{3x)}

\int \frac{6 x}{e ^{3 x}} d x

integral of (3+3cot(x))

\int (3 + 3 cot (x)) d x

integral of 7+5t+(3t^2)/2

\int 7 + 5 t + \frac{3 t ^{2}}{2} d t