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Beliebt Rechnen >

integral of (4x+1)^2

Lösung

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

Lösung

\frac{16 x ^{3}}{3} + 4 x^{2} + x + C

Schritte zur Lösung

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

Multipliziere aus

(4 x + 1)^{2} : 16 x^{2} + 8 x + 1

= \int 16 x^{2} + 8 x + 1 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 16 x^{2} d x + \int 8 x d x + \int 1 d x

\int 16 x^{2} d x = \frac{16 x ^{3}}{3}

\int 8 x d x = 4 x^{2}

\int 1 d x = x

= \frac{16 x ^{3}}{3} + 4 x^{2} + x

Füge eine Konstante zur Lösung hinzu

= \frac{16 x ^{3}}{3} + 4 x^{2} + x + C

Graph

Beliebte Beispiele

integral of 5/(x+4)

\int \frac{5}{x + 4} d x

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d er i v a t i v e f (x) = \frac{3 t - 1}{t - 2}

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\int - sin (\frac{x}{a}) d x

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(x, y) \to (0, 0) lim (\frac{x y cos ( y )}{3 x ^{2} + y ^{2}})

limit as x approaches 0 of 4

x \to 0 lim (4)