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Beliebt Rechnen >

integral from 1 to 2 of 1/(8-3x)

Lösung

\int_{1}^{2} \frac{1}{8 - 3 x} d x

Lösung

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

+1

Dezimale

0.30543 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{1}{8 - 3 x} d x

Wende U-Substitution an

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

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

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

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

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

Vereinfache

= \frac{1}{3} [ln ∣ u ∣]_{2}^{5}

Berechne die Grenzen:

ln (5) - ln (2)

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

Graph

Beliebte Beispiele

integral of 8x^3+12x+2

\int 8 x^{3} + 12 x + 2 d x

(\partial)/(\partial x)(x^2y^2-3y)

\frac{\partial}{\partial x} (x^{2} y^{2} - 3 y)

fläche f(x)=4x+8,0,8

a re a f (x) = 4 x + 8, 0, 8

sum from n=0 to infinity of (7n!)/(2^n)

n = 0 \sum \infty \frac{7 n !}{2 ^{n}}

tangent f(x)=1-x-x^2,\at x=0

t an g e n t f (x) = 1 - x - x^{2}, at x = 0