de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of ((x^3+2x^2-4)/(x^2))

Lösung

\int (\frac{x ^{3} + 2 x ^{2} - 4}{x ^{2}}) d x

Lösung

\frac{x ^{2}}{2} + 2 x + \frac{4}{x} + C

Schritte zur Lösung

\int \frac{x ^{3} + 2 x ^{2} - 4}{x ^{2}} d x

Multipliziere aus

\frac{x ^{3} + 2 x ^{2} - 4}{x ^{2}} : x + 2 - \frac{4}{x ^{2}}

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

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

\int 2 d x = 2 x

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

= \frac{x ^{2}}{2} + 2 x - (- \frac{4}{x})

Vereinfache

= \frac{x ^{2}}{2} + 2 x + \frac{4}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + 2 x + \frac{4}{x} + C

Graph

Beliebte Beispiele

integral from 1 to 2 of sqrt(x-1)

\int_{1}^{2} x - 1 d x

inverselaplace (3s)/((s^2+4))

in v erse l a pl a ce \frac{3 s}{( s ^{2} + 4 )}

y^{''''}+2y^{''}+y=0

y^{^{''''}} + 2 y^{^{''}} + y = 0

derivative of ((10/(4+x))^{1/2})

\frac{d}{d x} ((\frac{10}{4 + x})^{\frac{1}{2}})

derivative-1/4 x^4+6x^2

d er i v a t i v e - \frac{1}{4} x^{4} + 6 x^{2}