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Beliebt Rechnen >

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

Lösung

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

Lösung

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

+1

Dezimale

0.20273 \dots

Schritte zur Lösung

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

Faktorisiere

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

= \int_{2}^{3} \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_{2}^{3} \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}]_{2}^{3}

Vereinfache

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

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

Berechne die Grenzen:

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

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

Graph

Beliebte Beispiele

integral of (y-2)^2

\int (y - 2)^{2} d y

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

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

integral of+4e^{-7x}

\int + 4 e^{- 7 x} d x

(\partial)/(\partial x)(3ze^{xy})

\frac{\partial}{\partial x} (3 z e^{x y})

steigung (4.5)(2.3)

s l o p e (4.5) (2.3)