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Beliebt Rechnen >

integral from 1 to 2 of 5/(2x-1)

Lösung

\int_{1}^{2} \frac{5}{2 x - 1} d x

Lösung

\frac{5}{2} ln (3)

+1

Dezimale

2.74653 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{5}{2 x - 1} d x

Entferne die Konstante:

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

= 5 \cdot \int_{1}^{2} \frac{1}{2 x - 1} d x

Wende U-Substitution an

= 5 \cdot \int_{1}^{3} \frac{1}{2 u} d u

Entferne die Konstante:

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

= 5 \cdot \frac{1}{2} \cdot \int_{1}^{3} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 \cdot \frac{1}{2} [ln ∣ u ∣]_{1}^{3}

Vereinfache

5 \cdot \frac{1}{2} [ln ∣ u ∣]_{1}^{3} : \frac{5}{2} [ln ∣ u ∣]_{1}^{3}

= \frac{5}{2} [ln ∣ u ∣]_{1}^{3}

Berechne die Grenzen:

ln (3)

= \frac{5}{2} ln (3)

Graph

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