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Beliebt Rechnen >

integral of x/(2x^2+5x+2)

Lösung

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

Lösung

- \frac{1}{6} ln ∣ 2 x + 1 ∣ + \frac{2}{3} ln ∣ x + 2 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{x}{2 x ^{2} + 5 x + 2} : - \frac{1}{3 ( 2 x + 1 )} + \frac{2}{3 ( x + 2 )}

= \int - \frac{1}{3 ( 2 x + 1 )} + \frac{2}{3 ( x + 2 )} 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}{3 ( 2 x + 1 )} d x + \int \frac{2}{3 ( x + 2 )} d x

\int \frac{1}{3 ( 2 x + 1 )} d x = \frac{1}{6} ln ∣ 2 x + 1 ∣

\int \frac{2}{3 ( x + 2 )} d x = \frac{2}{3} ln ∣ x + 2 ∣

= - \frac{1}{6} ln ∣ 2 x + 1 ∣ + \frac{2}{3} ln ∣ x + 2 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{6} ln ∣ 2 x + 1 ∣ + \frac{2}{3} ln ∣ x + 2 ∣ + C

Graph

Beliebte Beispiele

limit as x approaches infinity of-28x^4

x \to \infty lim (- 28 x^{4})

implicit (dy)/(dx),xy^2=4

im pl i c i t \frac{d y}{d x}, x y^{2} = 4

integral of (2x)/((x+2)(x+1))

\int \frac{2 x}{( x + 2 ) ( x + 1 )} d x

(\partial)/(\partial x)(4x-2y)

\frac{\partial}{\partial x} (4 x - 2 y)

tangent y=4^x,(1,4)

t an g e n t y = 4^{x}, (1, 4)