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Beliebt Rechnen >

integral of ((2x^3+5x^2-2x)/x)

Lösung

\int (\frac{2 x ^{3} + 5 x ^{2} - 2 x}{x}) d x

Lösung

\frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 2 x + C

Schritte zur Lösung

\int \frac{2 x ^{3} + 5 x ^{2} - 2 x}{x} d x

Vereinfache

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

= \int 2 x^{2} + 5 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 2 x^{2} d x + \int 5 x d x - \int 2 d x

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

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

\int 2 d x = 2 x

= \frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 2 x

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{3}}{3} + \frac{5 x ^{2}}{2} - 2 x + C

Graph

Beliebte Beispiele

fläche sin(x),cos(x)-1

a re a sin (x), cos (x) - 1

integral from 1 to 5 of x^3-10x^2+29x-20

\int_{1}^{5} x^{3} - 10 x^{2} + 29 x - 20 d x

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

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

y^{^{'}} = y^{3}

limit as x approaches 2 of (x^3-3x^2+4)/(3x^3-18x^2+36x-24)

x \to 2 lim (\frac{x ^{3} - 3 x ^{2} + 4}{3 x ^{3} - 18 x ^{2} + 36 x - 24})