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Beliebt Rechnen >

integral of (x-3)/((x+8)(x-2))

Lösung

\int \frac{x - 3}{( x + 8 ) ( x - 2 )} d x

Lösung

\frac{11}{10} ln ∣ x + 8 ∣ - \frac{1}{10} ln ∣ x - 2 ∣ + C

Schritte zur Lösung

\int \frac{x - 3}{( x + 8 ) ( x - 2 )} d x

Ermittle den Partialbruch von

\frac{x - 3}{( x + 8 ) ( x - 2 )} : \frac{11}{10 ( x + 8 )} - \frac{1}{10 ( x - 2 )}

= \int \frac{11}{10 ( x + 8 )} - \frac{1}{10 ( 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{11}{10 ( x + 8 )} d x - \int \frac{1}{10 ( x - 2 )} d x

\int \frac{11}{10 ( x + 8 )} d x = \frac{11}{10} ln ∣ x + 8 ∣

\int \frac{1}{10 ( x - 2 )} d x = \frac{1}{10} ln ∣ x - 2 ∣

= \frac{11}{10} ln ∣ x + 8 ∣ - \frac{1}{10} ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{11}{10} ln ∣ x + 8 ∣ - \frac{1}{10} ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

derivative sqrt(a^2-x^2)

d er i v a t i v e a^{2} - x^{2}

derivative h(x)=(2x)/(sin(x))

d er i v a t i v e h (x) = \frac{2 x}{sin ( x )}

derivative of (x^2+x(6-x))

\frac{d}{d x} ((x^{2} + x) (6 - x))

integral of 1/(sqrt(7x+6))

\int \frac{1}{7 x + 6} d x

slopeintercept (2,4),(5,13)

s l o p e in t erce pt (2, 4), (5, 13)