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Beliebt Rechnen >

integral of 1/(x^3+9x)

Lösung

\int \frac{1}{x ^{3} + 9 x} d x

Lösung

\frac{1}{9} ln ∣ x ∣ - \frac{1}{18} ln x^{2} + 9 + C

Schritte zur Lösung

\int \frac{1}{x ^{3} + 9 x} d x

Ermittle den Partialbruch von

\frac{1}{x ^{3} + 9 x} : \frac{1}{9 x} - \frac{x}{9 ( x ^{2} + 9 )}

= \int \frac{1}{9 x} - \frac{x}{9 ( x ^{2} + 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{1}{9 x} d x - \int \frac{x}{9 ( x ^{2} + 9 )} d x

\int \frac{1}{9 x} d x = \frac{1}{9} ln ∣ x ∣

\int \frac{x}{9 ( x ^{2} + 9 )} d x = \frac{1}{18} ln x^{2} + 9

= \frac{1}{9} ln ∣ x ∣ - \frac{1}{18} ln x^{2} + 9

Füge eine Konstante zur Lösung hinzu

= \frac{1}{9} ln ∣ x ∣ - \frac{1}{18} ln x^{2} + 9 + C

Graph

Beliebte Beispiele

tangent 5sec(x),\at x= pi/3

t an g e n t 5 sec (x), at x = \frac{π}{3}

fläche-x^2+3x,2x^3-x^2-5x

a re a - x^{2} + 3 x, 2 x^{3} - x^{2} - 5 x

limit as x approaches 0 of ((x-1))/x

x \to 0 lim (\frac{( x - 1 )}{x})

integral of y/((y^2+z^2)^{3/2)}

\int \frac{y}{( y ^{2} + z ^{2} ) ^{\frac{3}{2}}} d y

steigung (1,7),(7,3)

s l o p e (1, 7), (7, 3)