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Beliebt Rechnen >

integral of 1/((x-7)(x+1))

Lösung

\int \frac{1}{( x - 7 ) ( x + 1 )} d x

Lösung

\frac{1}{8} ln ∣ x - 7 ∣ - \frac{1}{8} ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int \frac{1}{( x - 7 ) ( x + 1 )} d x

Ermittle den Partialbruch von

\frac{1}{( x - 7 ) ( x + 1 )} : \frac{1}{8 ( x - 7 )} - \frac{1}{8 ( x + 1 )}

= \int \frac{1}{8 ( x - 7 )} - \frac{1}{8 ( x + 1 )} 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}{8 ( x - 7 )} d x - \int \frac{1}{8 ( x + 1 )} d x

\int \frac{1}{8 ( x - 7 )} d x = \frac{1}{8} ln ∣ x - 7 ∣

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

= \frac{1}{8} ln ∣ x - 7 ∣ - \frac{1}{8} ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{8} ln ∣ x - 7 ∣ - \frac{1}{8} ln ∣ x + 1 ∣ + C

Graph

Beliebte Beispiele

derivative of e^{3ln(x^2})

\frac{d}{d x} (e^{3 l n (x^{2})})

integral of (1/((x-7)^2))

\int (\frac{1}{( x - 7 ) ^{2}}) d x

limit as x approaches 0 of sin(-x^2)

x \to 0 lim (sin (- x^{2}))

integral of pi(x^2-x^4)

\int π (x^{2} - x^{4}) d x

integral of (sin(ln(y)))/y

\int \frac{sin ( ln ( y ) )}{y} d y