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Beliebt Rechnen >

integral from 4 to 5 of 1/(5x-1)

Lösung

\int_{4}^{5} \frac{1}{5 x - 1} d x

Lösung

\frac{1}{5} (ln (24) - ln (19))

+1

Dezimale

0.04672 \dots

Schritte zur Lösung

\int_{4}^{5} \frac{1}{5 x - 1} d x

Wende U-Substitution an

= \int_{19}^{24} \frac{1}{5 u} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{19}^{24} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} [ln ∣ u ∣]_{19}^{24}

Berechne die Grenzen:

ln (24) - ln (19)

= \frac{1}{5} (ln (24) - ln (19))

Graph

Beliebte Beispiele

xy^'+3y=(4e^{2x})/(x^2)

x y^{^{'}} + 3 y = \frac{4 e ^{2 x}}{x ^{2}}

limit as x approaches 1 of (2x)/(x-1)

x \to 1 lim (\frac{2 x}{x - 1})

derivative f(x)=9x^5(x^3-2x)

d er i v a t i v e f (x) = 9 x^{5} (x^{3} - 2 x)

y^{''}-2y^'-63y=0

y^{^{''}} - 2 y^{^{'}} - 63 y = 0

sum from n=1 to infinity of 1/(n^{-1)}

n = 1 \sum \infty \frac{1}{n ^{- 1}}