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Beliebt Rechnen >

integral from 0 to 2 of 2/(x+1)

Lösung

\int_{0}^{2} \frac{2}{x + 1} d x

Lösung

2 ln (3)

+1

Dezimale

2.19722 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{2}{x + 1} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{2} \frac{1}{x + 1} d x

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 [ln ∣ u ∣]_{1}^{3}

Berechne die Grenzen:

ln (3)

= 2 ln (3)

Graph

Beliebte Beispiele

integral from 2 to 6 of x^2+7

\int_{2}^{6} x^{2} + 7 d x

integral from-pi to 0 of (pi+x)sin(nx)

\int_{- π}^{0} (π + x) sin (n x) d x

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

\int_{- 1}^{1} 2^{x} - (\frac{1}{2})^{x} d x

integral from 3 to 7 of 7x

\int_{3}^{7} 7 x d x

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\int_{- 4}^{4} (∣ x ∣) d x