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Beliebt Rechnen >

integral from-1 to 1 of (13-12u)^{-1}

Lösung

\int_{- 1}^{1} (13 - 12 u)^{- 1} d u

Lösung

\frac{1}{6} ln (5)

+1

Dezimale

0.26823 \dots

Schritte zur Lösung

\int_{- 1}^{1} (13 - 12 u)^{- 1} d u

Wende Exponentenregel an:

a^{- 1} = \frac{1}{a}

= \int_{- 1}^{1} \frac{1}{13 - 12 u} d u

Wende U-Substitution an

= \int_{25}^{1} - \frac{1}{12 v} d v

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{25} - \frac{1}{12 v} d v

Entferne die Konstante:

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

= - (- \frac{1}{12} \cdot \int_{1}^{25} \frac{1}{v} d v)

Nutze das gemeinsame Integral :

\int \frac{1}{v} d v = ln (∣ v ∣)

= - (- \frac{1}{12} [ln ∣ v ∣]_{1}^{25})

Vereinfache

= \frac{1}{12} [ln ∣ v ∣]_{1}^{25}

Berechne die Grenzen:

2 ln (5)

= \frac{1}{12} \cdot 2 ln (5)

Vereinfache

= \frac{1}{6} ln (5)

Graph

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