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Beliebt Rechnen >

integral of (x-48)/((x+2)(x-3))

Lösung

\int \frac{x - 48}{( x + 2 ) ( x - 3 )} d x

Lösung

10 ln ∣ x + 2 ∣ - 9 ln ∣ x - 3 ∣ + C

Schritte zur Lösung

\int \frac{x - 48}{( x + 2 ) ( x - 3 )} d x

Ermittle den Partialbruch von

\frac{x - 48}{( x + 2 ) ( x - 3 )} : \frac{10}{x + 2} - \frac{9}{x - 3}

= \int \frac{10}{x + 2} - \frac{9}{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{10}{x + 2} d x - \int \frac{9}{x - 3} d x

\int \frac{10}{x + 2} d x = 10 ln ∣ x + 2 ∣

\int \frac{9}{x - 3} d x = 9 ln ∣ x - 3 ∣

= 10 ln ∣ x + 2 ∣ - 9 ln ∣ x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= 10 ln ∣ x + 2 ∣ - 9 ln ∣ x - 3 ∣ + C

Graph

Beliebte Beispiele

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

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

integral of (-9x+27)/((x^2+2x+4)^2)

\int \frac{- 9 x + 27}{( x ^{2} + 2 x + 4 ) ^{2}} d x

integral of 7/(6x+8)

\int \frac{7}{6 x + 8} d x

integral of (x-2)/(x^2+4x+13)

\int \frac{x - 2}{x ^{2} + 4 x + 13} d x

integral of 6x^2-4x+3

\int 6 x^{2} - 4 x + 3 d x