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Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x ∣ - \frac{2}{3} arctan (\frac{x}{3}) + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{2}{x ^{2} + 3} d x = \frac{2}{3} arctan (\frac{x}{3})

= ln ∣ x ∣ - \frac{2}{3} arctan (\frac{x}{3})

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - \frac{2}{3} arctan (\frac{x}{3}) + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(1/(y^2))

\frac{\partial}{\partial x} (\frac{1}{y ^{2}})

xdx+ye^{-x}dy=0,y(0)=1

x d x + y e^{- x} d y = 0, y (0) = 1

(d^2y)/(dx^2)-4(dy)/(dx)+3y=0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 3 y = 0

y=cos(sin(sqrt(2x+5)))

y = cos (sin (2 x + 5))

integral of sec^2(7x)

\int sec^{2} (7 x) d x