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Beliebt Rechnen >

integral from 2 to 3 of 1/(4-3x)

Lösung

\int_{2}^{3} \frac{1}{4 - 3 x} d x

Lösung

\frac{1}{3} (ln (2) - ln (5))

+1

Dezimale

- 0.30543 \dots

Schritte zur Lösung

\int_{2}^{3} \frac{1}{4 - 3 x} d x

Wende U-Substitution an

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

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

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

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

Vereinfache

= \frac{1}{3} [ln ∣ u ∣]_{- 5}^{- 2}

Berechne die Grenzen:

ln (2) - ln (5)

= \frac{1}{3} (ln (2) - ln (5))

Graph

Beliebte Beispiele

integral of-3cos(x)

\int - 3 cos (x) d x

derivative of x^7(x-12^5)

\frac{d}{d x} (x^{7} (x - 12)^{5})

(dy)/(dx)= 1/(x-x^3)

\frac{d y}{d x} = \frac{1}{x - x ^{3}}

(\partial)/(\partial x)(2x-3y+5z)

\frac{\partial}{\partial x} (2 x - 3 y + 5 z)

integral of 3^{2x}cos^2(3^x)

\int 3^{2 x} cos^{2} (3^{x}) d x