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Beliebt Rechnen >

integral of ((4x-11))/((x^3-9x^2))

Lösung

\int \frac{( 4 x - 11 )}{( x ^{3} - 9 x ^{2} )} d x

Lösung

- \frac{25}{81} ln ∣ x ∣ - \frac{11}{9 x} + \frac{25}{81} ln ∣ x - 9 ∣ + C

Schritte zur Lösung

\int \frac{4 x - 11}{x ^{3} - 9 x ^{2}} d x

Ermittle den Partialbruch von

\frac{4 x - 11}{x ^{3} - 9 x ^{2}} : - \frac{25}{81 x} + \frac{11}{9 x ^{2}} + \frac{25}{81 ( x - 9 )}

= \int - \frac{25}{81 x} + \frac{11}{9 x ^{2}} + \frac{25}{81 ( 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

= - \int \frac{25}{81 x} d x + \int \frac{11}{9 x ^{2}} d x + \int \frac{25}{81 ( x - 9 )} d x

\int \frac{25}{81 x} d x = \frac{25}{81} ln ∣ x ∣

\int \frac{11}{9 x ^{2}} d x = - \frac{11}{9 x}

\int \frac{25}{81 ( x - 9 )} d x = \frac{25}{81} ln ∣ x - 9 ∣

= - \frac{25}{81} ln ∣ x ∣ - \frac{11}{9 x} + \frac{25}{81} ln ∣ x - 9 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{25}{81} ln ∣ x ∣ - \frac{11}{9 x} + \frac{25}{81} ln ∣ x - 9 ∣ + C

Graph

Beliebte Beispiele

derivative of cos(wt+sin(wt))

\frac{d}{d x} (cos (wt) + sin (wt))

sum from n=5 to infinity of 1/(n+25)

n = 5 \sum \infty \frac{1}{n + 25}

y^'=ky(4000-y),y(0)=150

y^{^{'}} = k y (4000 - y), y (0) = 150

derivative of 5/(x-4)

\frac{d}{d x} (\frac{5}{x - 4})

y^{''}+y=csc(x)

y^{^{''}} + y = csc (x)