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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (sqrt(1-x^3))/(x^2sqrt(x))

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

integral of xsqrt(29x-7)

\int x 29 x - 7 d x

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\int cos (9 x - 20) cos (5 x + 20) d x

integral of e^{(3x)/4}

\int e^{\frac{3 x}{4}} d x

integral of sqrt((2x+21))

\int (2 x + 21) d x