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Beliebt Rechnen >

integral from 3 to 8 of 1/(x^2-1)

Lösung

\int_{3}^{8} \frac{1}{x ^{2} - 1} d x

Lösung

- \frac{2 ln ( 3 ) - ln ( 14 )}{2}

+1

Dezimale

0.22091 \dots

Schritte zur Lösung

\int_{3}^{8} \frac{1}{x ^{2} - 1} d x

Faktorisiere

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

= \int_{3}^{8} \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_{3}^{8} \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}]_{3}^{8}

Vereinfache

- [\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{3}^{8} : - [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{3}^{8}

= - [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{3}^{8}

Berechne die Grenzen:

\frac{2 ln ( 3 ) - ln ( 7 ) - ln ( 2 )}{2}

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

Vereinfache

= - \frac{2 ln ( 3 ) - ln ( 14 )}{2}

Graph

Beliebte Beispiele

tangent y=x^2-6

t an g e n t y = x^{2} - 6

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x \to \infty lim (0 + x)

d/(dc)((sin(2c))/(2-cos(2c)))

\frac{d}{d c} (\frac{sin ( 2 c )}{2 - cos ( 2 c )})

integral of 3/(sqrt(1-9x^2))

\int \frac{3}{1 - 9 x ^{2}} d x

integral of (x^2-3x-4)

\int (x^{2} - 3 x - 4) d x