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Beliebt Rechnen >

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

Lösung

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

Lösung

16 x^{7} - 16 x^{5} + 4 x^{3} - \frac{96 x ^{7}}{7} + \frac{64 x ^{5}}{5} - \frac{8 x ^{3}}{3} + C

Schritte zur Lösung

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

Faktorisiere

4 x^{2} - 2 : - (- 4 x^{2} + 2)

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

(- (- 4 x^{2} + 2))^{2} = (- 4 x^{2} + 2)^{2}

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

Wende die partielle Integration an

= x^{3} (- 4 x^{2} + 2)^{2} - \int x (96 x^{5} - 64 x^{3} + 8 x) d x

\int x (96 x^{5} - 64 x^{3} + 8 x) d x = \frac{96 x ^{7}}{7} - \frac{64 x ^{5}}{5} + \frac{8 x ^{3}}{3}

= x^{3} (- 4 x^{2} + 2)^{2} - (\frac{96 x ^{7}}{7} - \frac{64 x ^{5}}{5} + \frac{8 x ^{3}}{3})

Vereinfache

x^{3} (- 4 x^{2} + 2)^{2} - (\frac{96 x ^{7}}{7} - \frac{64 x ^{5}}{5} + \frac{8 x ^{3}}{3}) : 16 x^{7} - 16 x^{5} + 4 x^{3} - \frac{96 x ^{7}}{7} + \frac{64 x ^{5}}{5} - \frac{8 x ^{3}}{3}

= 16 x^{7} - 16 x^{5} + 4 x^{3} - \frac{96 x ^{7}}{7} + \frac{64 x ^{5}}{5} - \frac{8 x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= 16 x^{7} - 16 x^{5} + 4 x^{3} - \frac{96 x ^{7}}{7} + \frac{64 x ^{5}}{5} - \frac{8 x ^{3}}{3} + C

Graph

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