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Beliebt Rechnen >

integral from-3 to 3 of (18)/(x^2-6x-72)

Lösung

\int_{- 3}^{3} \frac{18}{x ^{2} - 6 x - 72} d x

Lösung

- ln (3) + ln (\frac{3}{5})

+1

Dezimale

- 1.60943 \dots

Schritte zur Lösung

\int_{- 3}^{3} \frac{18}{x ^{2} - 6 x - 72} d x

Entferne die Konstante:

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

= 18 \cdot \int_{- 3}^{3} \frac{1}{x ^{2} - 6 x - 72} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} - 6 x - 72} : - \frac{1}{18 ( x + 6 )} + \frac{1}{18 ( x - 12 )}

= 18 \cdot \int_{- 3}^{3} - \frac{1}{18 ( x + 6 )} + \frac{1}{18 ( x - 12 )} 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

= 18 (- \int_{- 3}^{3} \frac{1}{18 ( x + 6 )} d x + \int_{- 3}^{3} \frac{1}{18 ( x - 12 )} d x)

\int_{- 3}^{3} \frac{1}{18 ( x + 6 )} d x = \frac{1}{18} ln (3)

\int_{- 3}^{3} \frac{1}{18 ( x - 12 )} d x = \frac{1}{18} ln (\frac{3}{5})

= 18 (- \frac{1}{18} ln (3) + \frac{1}{18} ln (\frac{3}{5}))

Vereinfache

18 (- \frac{1}{18} ln (3) + \frac{1}{18} ln (\frac{3}{5})) : - ln (3) + ln (\frac{3}{5})

= - ln (3) + ln (\frac{3}{5})

Graph

Beliebte Beispiele

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

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

derivative f(x)=e^t

d er i v a t i v e f (x) = e^{t}

tangent y=sqrt(2x+1),(4,3)

t an g e n t y = 2 x + 1, (4, 3)

integral of (x^2)/(e^{x/3)}

\int \frac{x ^{2}}{e ^{\frac{x}{3}}} d x

laplacetransform 5*t

l a pl a ce t r an s f or m 5 \cdot t