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Beliebt Rechnen >

integral from 0 to 1 of (x-6)/(x^2-6x+8)

Lösung

\int_{0}^{1} \frac{x - 6}{x ^{2} - 6 x + 8} d x

Lösung

- ln (3)

+1

Dezimale

- 1.09861 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x - 6}{x ^{2} - 6 x + 8} d x

Ermittle den Partialbruch von

\frac{x - 6}{x ^{2} - 6 x + 8} : \frac{2}{x - 2} - \frac{1}{x - 4}

= \int_{0}^{1} \frac{2}{x - 2} - \frac{1}{x - 4} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} \frac{2}{x - 2} d x - \int_{0}^{1} \frac{1}{x - 4} d x

\int_{0}^{1} \frac{2}{x - 2} d x = - 2 ln (2)

\int_{0}^{1} \frac{1}{x - 4} d x = ln (3) - 2 ln (2)

= - 2 ln (2) - (ln (3) - 2 ln (2))

Vereinfache

= - ln (3)

Graph

Beliebte Beispiele

3x(dy)/(dx)=sqrt(x^2-4)

3 x \frac{d y}{d x} = x^{2} - 4

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integral from-infinity to 6 of re^{r/2}

\int_{- \infty}^{6} r e^{\frac{r}{2}} d r

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\frac{\partial}{\partial x} (4 y^{3})

(dy)/(dt)=3y+e^{7t}

\frac{d y}{d t} = 3 y + e^{7 t}