integral of (2x^3-1)^2

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

(2 x^{3} - 1)^{2} : 4 x^{6} - 4 x^{3} + 1

= \int 4 x^{6} - 4 x^{3} + 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 4 x^{6} d x - \int 4 x^{3} d x + \int 1 d x

\int 4 x^{6} d x = \frac{4 x ^{7}}{7}

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

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

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

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