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Beliebt Rechnen >

integral of 1/((x+1)(x+5))

Lösung

\int \frac{1}{( x + 1 ) ( x + 5 )} d x

Lösung

\frac{1}{4} ln ∣ x + 1 ∣ - \frac{1}{4} ln ∣ x + 5 ∣ + C

Schritte zur Lösung

\int \frac{1}{( x + 1 ) ( x + 5 )} d x

Ermittle den Partialbruch von

\frac{1}{( x + 1 ) ( x + 5 )} : \frac{1}{4 ( x + 1 )} - \frac{1}{4 ( x + 5 )}

= \int \frac{1}{4 ( x + 1 )} - \frac{1}{4 ( x + 5 )} 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{1}{4 ( x + 1 )} d x - \int \frac{1}{4 ( x + 5 )} d x

\int \frac{1}{4 ( x + 1 )} d x = \frac{1}{4} ln ∣ x + 1 ∣

\int \frac{1}{4 ( x + 5 )} d x = \frac{1}{4} ln ∣ x + 5 ∣

= \frac{1}{4} ln ∣ x + 1 ∣ - \frac{1}{4} ln ∣ x + 5 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} ln ∣ x + 1 ∣ - \frac{1}{4} ln ∣ x + 5 ∣ + C

Graph

Beliebte Beispiele

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d er i v a t i v e y = cos (a^{9} + x^{9})

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slopeintercept (8.1)(4.1)

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(\partial)/(\partial y)(x^4+2x^2y)

\frac{\partial}{\partial y} (x^{4} + 2 x^{2} y)

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n = 0 \sum \infty n \cdot sin (n \cdot π)