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Beliebt Rechnen >

integral from 1 to 8 of 3/x

Lösung

\int_{1}^{8} \frac{3}{x} d x

Lösung

9 ln (2)

+1

Dezimale

6.23832 \dots

Schritte zur Lösung

\int_{1}^{8} \frac{3}{x} d x

Entferne die Konstante:

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

= 3 \cdot \int_{1}^{8} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= 3 [ln ∣ x ∣]_{1}^{8}

Berechne die Grenzen:

3 ln (2)

= 3 \cdot 3 ln (2)

Vereinfache

= 9 ln (2)

Graph

Beliebte Beispiele

derivative of e^{x^{1/2}}

\frac{d}{d x} (e^{x^{\frac{1}{2}}})

tangent f(x)=2x^3-3x^2+3,\at x=1

t an g e n t f (x) = 2 x^{3} - 3 x^{2} + 3, at x = 1

derivative of 2-2x

\frac{d}{d x} (2 - 2 x)

derivative of x^{-ln(x})

\frac{d}{d x} (x^{- l n (x)})

integral of sin^2(2t)cos(2t)

\int sin^{2} (2 t) cos (2 t) d t