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Beliebt Rechnen >

integral from 8 to 9 of 1/(x^2-1)

Lösung

\int_{8}^{9} \frac{1}{x ^{2} - 1} d x

Lösung

- \frac{ln ( \frac{5}{4} ) - 2 ln ( 3 ) + ln ( 7 )}{2}

+1

Dezimale

0.01408 \dots

Schritte zur Lösung

\int_{8}^{9} \frac{1}{x ^{2} - 1} d x

Faktorisiere

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

= \int_{8}^{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_{8}^{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}]_{8}^{9}

Vereinfache

- [\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{8}^{9} : - [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{8}^{9}

= - [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{8}^{9}

Berechne die Grenzen:

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

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

Vereinfache

= - \frac{ln ( \frac{5}{4} ) - 2 ln ( 3 ) + ln ( 7 )}{2}

Graph

Beliebte Beispiele

fläche y=sqrt(9-x^2),0<= x<= 2

a re a y = 9 - x^{2}, 0 \leq x \leq 2

tangent f(x)=7e^{x^2-9x+8},\at x=0

t an g e n t f (x) = 7 e^{x^{2} - 9 x + 8}, at x = 0

derivative y=164sqrt(4x^4)+4

d er i v a t i v e y = 164 4 x^{4} + 4

y^{''}+6y^'+5y=10

y^{^{''}} + 6 y^{^{'}} + 5 y = 10

integral of 1/h

\int \frac{1}{h} d h