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Beliebt Rechnen >

integral of ((x^2-x+36))/(x^3+6x)

Lösung

\int \frac{( x ^{2} - x + 36 )}{x ^{3} + 6 x} d x

Lösung

6 ln ∣ x ∣ - \frac{5}{2} ln x^{2} + 6 - \frac{1}{6} arctan (\frac{x}{6}) + C

Schritte zur Lösung

\int \frac{x ^{2} - x + 36}{x ^{3} + 6 x} d x

Ermittle den Partialbruch von

\frac{x ^{2} - x + 36}{x ^{3} + 6 x} : \frac{6}{x} + \frac{- 5 x - 1}{x ^{2} + 6}

= \int \frac{6}{x} + \frac{- 5 x - 1}{x ^{2} + 6} 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{6}{x} d x + \int \frac{- 5 x - 1}{x ^{2} + 6} d x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

\int \frac{- 5 x - 1}{x ^{2} + 6} d x = - \frac{5}{2} ln x^{2} + 6 - \frac{1}{6} arctan (\frac{x}{6})

= 6 ln ∣ x ∣ - \frac{5}{2} ln x^{2} + 6 - \frac{1}{6} arctan (\frac{x}{6})

Füge eine Konstante zur Lösung hinzu

= 6 ln ∣ x ∣ - \frac{5}{2} ln x^{2} + 6 - \frac{1}{6} arctan (\frac{x}{6}) + C

Graph

Beliebte Beispiele

tangent y=2sin(x),(pi/6 ,1)

t an g e n t y = 2 sin (x), (\frac{π}{6}, 1)

derivative 1-(1-0.01x)^3

d er i v a t i v e 1 - (1 - 0.01 x)^{3}

sum from n=1 to infinity of n^{3/4}

n = 1 \sum \infty n^{\frac{3}{4}}

integral of 90x^2sin(2+6x^3)

\int 90 x^{2} sin (2 + 6 x^{3}) d x

sqrt(1-y^2)dx-sqrt(1-x^2)dy=0

1 - y^{2} d x - 1 - x^{2} d y = 0