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Beliebt Rechnen >

integral of (5x^3+2x^2-6x+3)

Lösung

\int (5 x^{3} + 2 x^{2} - 6 x + 3) d x

Lösung

\frac{5 x ^{4}}{4} + \frac{2 x ^{3}}{3} - 3 x^{2} + 3 x + C

Schritte zur Lösung

\int 5 x^{3} + 2 x^{2} - 6 x + 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 5 x^{3} d x + \int 2 x^{2} d x - \int 6 x d x + \int 3 d x

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

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

\int 6 x d x = 3 x^{2}

\int 3 d x = 3 x

= \frac{5 x ^{4}}{4} + \frac{2 x ^{3}}{3} - 3 x^{2} + 3 x

Füge eine Konstante zur Lösung hinzu

= \frac{5 x ^{4}}{4} + \frac{2 x ^{3}}{3} - 3 x^{2} + 3 x + C

Graph

Beliebte Beispiele

(dy)/(dt)-2ty=1

\frac{d y}{d t} - 2 t y = 1

limit as x approaches 3-of 2x+1

x \to 3 - lim (2 x + 1)

fläche y=6x^4-6x^2,y=3x^2,x=0

a re a y = 6 x^{4} - 6 x^{2}, y = 3 x^{2}, x = 0

(dy)/(dt)+e^ty=10e^t

\frac{d y}{d t} + e^{t} y = 10 e^{t}

integral of (x^2-x+5)/(x-1)

\int \frac{x ^{2} - x + 5}{x - 1} d x