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Beliebt Rechnen >

integral of x(1+2x)^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

x (1 + 2 x)^{2} : x + 4 x^{2} + 4 x^{3}

= \int x + 4 x^{2} + 4 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 x d x + \int 4 x^{2} d x + \int 4 x^{3} d x

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

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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