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Beliebt Rechnen >

integral of (x^4+x-4)/(x^2+2)

Lösung

\int \frac{x ^{4} + x - 4}{x ^{2} + 2} d x

Lösung

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

Schritte zur Lösung

\int \frac{x ^{4} + x - 4}{x ^{2} + 2} d x

Lange Division

\frac{x ^{4} + x - 4}{x ^{2} + 2} : x^{2} - 2 + \frac{x}{x ^{2} + 2}

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

\int x^{2} d x = \frac{x ^{3}}{3}

\int 2 d x = 2 x

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of x/(sqrt(x^2+64))

\frac{d}{d x} (\frac{x}{x ^{2} + 64})

(dy)/(dx)(x^2)=y^3

\frac{d y}{d x} (x^{2}) = y^{3}

integral of 1/(\sqrt[3]{t^2)}

\int \frac{1}{3 t ^{2}} d t

integral of (e^a+1)/(e^a)

\int \frac{e ^{a} + 1}{e ^{a}} d a

limit as x approaches-8 of (x^2-4)/(8-x)

x \to - 8 lim (\frac{x ^{2} - 4}{8 - x})