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Beliebt Rechnen >

integral of x(2+x^3)^2

Lösung

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

Lösung

2 x^{2} + \frac{4 x ^{5}}{5} + \frac{x ^{8}}{8} + C

Schritte zur Lösung

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

Multipliziere aus

x (2 + x^{3})^{2} : 4 x + 4 x^{4} + x^{7}

= \int 4 x + 4 x^{4} + x^{7} 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 4 x d x + \int 4 x^{4} d x + \int x^{7} d x

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

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

\int x^{7} d x = \frac{x ^{8}}{8}

= 2 x^{2} + \frac{4 x ^{5}}{5} + \frac{x ^{8}}{8}

Füge eine Konstante zur Lösung hinzu

= 2 x^{2} + \frac{4 x ^{5}}{5} + \frac{x ^{8}}{8} + C

Graph

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