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Beliebt Rechnen >

integral of x(3x^2+1)

Lösung

\int x (3 x^{2} + 1) d x

Lösung

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

Schritte zur Lösung

\int x (3 x^{2} + 1) d x

Multipliziere aus

x (3 x^{2} + 1) : 3 x^{3} + x

= \int 3 x^{3} + x 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 3 x^{3} d x + \int x d x

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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(dy)/(dt)+2/t y=4t-3+2/t

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limit as x approaches 10 of (sqrt(x-1)-3)/(x-10)

x \to 10 lim (\frac{x - 1 - 3}{x - 10})