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Beliebt Rechnen >

integral from-3 to 3 of (14)/(x^2-4x-45)

Lösung

\int_{- 3}^{3} \frac{14}{x ^{2} - 4 x - 45} d x

Lösung

- 3 ln (2)

+1

Dezimale

- 2.07944 \dots

Schritte zur Lösung

\int_{- 3}^{3} \frac{14}{x ^{2} - 4 x - 45} d x

Entferne die Konstante:

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

= 14 \cdot \int_{- 3}^{3} \frac{1}{x ^{2} - 4 x - 45} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} - 4 x - 45} : - \frac{1}{14 ( x + 5 )} + \frac{1}{14 ( x - 9 )}

= 14 \cdot \int_{- 3}^{3} - \frac{1}{14 ( x + 5 )} + \frac{1}{14 ( x - 9 )} 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

= 14 (- \int_{- 3}^{3} \frac{1}{14 ( x + 5 )} d x + \int_{- 3}^{3} \frac{1}{14 ( x - 9 )} d x)

\int_{- 3}^{3} \frac{1}{14 ( x + 5 )} d x = \frac{1}{7} ln (2)

\int_{- 3}^{3} \frac{1}{14 ( x - 9 )} d x = - \frac{1}{14} ln (2)

= 14 (- \frac{1}{7} ln (2) - \frac{1}{14} ln (2))

Vereinfache

14 (- \frac{1}{7} ln (2) - \frac{1}{14} ln (2)) : - 3 ln (2)

= - 3 ln (2)

Graph

Beliebte Beispiele

derivative y=(3sqrt(x)+5)x^2

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\int \frac{x ^{2} + 5 x + 6}{x + 3} d x

fläche y=9-x^2,y=x+3

a re a y = 9 - x^{2}, y = x + 3

integral of sin(6x)

\int sin (6 x) d x

(-7sqrt(2)sin(t))^'

(- 72 sin (t))^{^{'}}