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Beliebt Rechnen >

integral from 6 to 9 of 1/(x^2-1)

Lösung

\int_{6}^{9} \frac{1}{x ^{2} - 1} d x

Lösung

- \frac{ln ( \frac{5}{4} ) - ln ( 7 ) + ln ( 5 )}{2}

+1

Dezimale

0.05666 \dots

Schritte zur Lösung

\int_{6}^{9} \frac{1}{x ^{2} - 1} d x

Faktorisiere

x^{2} - 1 : - (- x^{2} + 1)

= \int_{6}^{9} \frac{1}{- ( - x ^{2} + 1 )} d x

Entferne die Konstante:

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

= - \int_{6}^{9} \frac{1}{- x ^{2} + 1} d x

Nutze das gemeinsame Integral :

\int \frac{1}{- x ^{2} + 1} d x = \frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}

= - [\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{6}^{9}

Vereinfache

- [\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{6}^{9} : - [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{6}^{9}

= - [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{6}^{9}

Berechne die Grenzen:

\frac{ln ( 10 ) - 3 ln ( 2 ) - ln ( 7 ) + ln ( 5 )}{2}

= - \frac{ln ( 10 ) - 3 ln ( 2 ) - ln ( 7 ) + ln ( 5 )}{2}

Vereinfache

= - \frac{ln ( \frac{5}{4} ) - ln ( 7 ) + ln ( 5 )}{2}

Graph

Beliebte Beispiele

integral of e^{-sx}sin(ax)

\int e^{- s x} sin (a x) d x

integral of e^{x^1}

\int e^{x^{1}} d x

integral of sin(x)-2

\int sin (x) - 2 d x

limit as x approaches 1 of sqrt(x+5)

x \to 1 lim (x + 5)

derivative of (3x-1^5(2x+3)^4)

\frac{d}{d x} ((3 x - 1)^{5} (2 x + 3)^{4})