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Beliebt Rechnen >

integral of (11)/((x-3)(x+8))

Lösung

\int \frac{11}{( x - 3 ) ( x + 8 )} d x

Lösung

ln ∣ x - 3 ∣ - ln ∣ x + 8 ∣ + C

Schritte zur Lösung

\int \frac{11}{( x - 3 ) ( x + 8 )} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 11 \cdot \int \frac{1}{( x - 3 ) ( x + 8 )} d x

Ermittle den Partialbruch von

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

= 11 \cdot \int \frac{1}{11 ( x - 3 )} - \frac{1}{11 ( x + 8 )} 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

= 11 (\int \frac{1}{11 ( x - 3 )} d x - \int \frac{1}{11 ( x + 8 )} d x)

\int \frac{1}{11 ( x - 3 )} d x = \frac{1}{11} ln ∣ x - 3 ∣

\int \frac{1}{11 ( x + 8 )} d x = \frac{1}{11} ln ∣ x + 8 ∣

= 11 (\frac{1}{11} ln ∣ x - 3 ∣ - \frac{1}{11} ln ∣ x + 8 ∣)

Vereinfache

11 (\frac{1}{11} ln ∣ x - 3 ∣ - \frac{1}{11} ln ∣ x + 8 ∣) : ln ∣ x - 3 ∣ - ln ∣ x + 8 ∣

= ln ∣ x - 3 ∣ - ln ∣ x + 8 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x - 3 ∣ - ln ∣ x + 8 ∣ + C

Graph

Beliebte Beispiele

integral of 7sqrt(y)

\int 7 y d y

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

\int \frac{3 x + 4}{2 x} d x

integral of (e^{2x})/(2x)

\int \frac{e ^{2 x}}{2 x} d x

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

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

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

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