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Beliebt Rechnen >

integral of (4x^3-2)^2

Lösung

\int (4 x^{3} - 2)^{2} d x

Lösung

\frac{16 x ^{7}}{7} - 4 x^{4} + 4 x + C

Schritte zur Lösung

\int (4 x^{3} - 2)^{2} d x

Multipliziere aus

(4 x^{3} - 2)^{2} : 16 x^{6} - 16 x^{3} + 4

= \int 16 x^{6} - 16 x^{3} + 4 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^{6} d x - \int 16 x^{3} d x + \int 4 d x

\int 16 x^{6} d x = \frac{16 x ^{7}}{7}

\int 16 x^{3} d x = 4 x^{4}

\int 4 d x = 4 x

= \frac{16 x ^{7}}{7} - 4 x^{4} + 4 x

Füge eine Konstante zur Lösung hinzu

= \frac{16 x ^{7}}{7} - 4 x^{4} + 4 x + C

Graph

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