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Beliebt Rechnen >

integral of 4x(2x-1)(4x+1)

Lösung

\int 4 x (2 x - 1) (4 x + 1) d x

Lösung

4 (\frac{8 x ^{4}}{3} + x^{3} - \frac{4 x ^{3}}{3} - \frac{x ^{2}}{2} - \frac{2 x ^{4}}{3} - \frac{x ^{3}}{3}) + C

Schritte zur Lösung

\int 4 x (2 x - 1) (4 x + 1) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int x (2 x - 1) (4 x + 1) d x

Wende die partielle Integration an

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

\int \frac{8 x ^{3}}{3} + x^{2} d x = \frac{2 x ^{4}}{3} + \frac{x ^{3}}{3}

= 4 (\frac{8 x ^{4}}{3} + x^{3} - \frac{4 x ^{3}}{3} - \frac{x ^{2}}{2} - (\frac{2 x ^{4}}{3} + \frac{x ^{3}}{3}))

Vereinfache

= 4 (\frac{8 x ^{4}}{3} + x^{3} - \frac{4 x ^{3}}{3} - \frac{x ^{2}}{2} - \frac{2 x ^{4}}{3} - \frac{x ^{3}}{3})

Füge eine Konstante zur Lösung hinzu

= 4 (\frac{8 x ^{4}}{3} + x^{3} - \frac{4 x ^{3}}{3} - \frac{x ^{2}}{2} - \frac{2 x ^{4}}{3} - \frac{x ^{3}}{3}) + C

Graph

Beliebte Beispiele

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\int (4 x - 1) \cdot ln (x) d x

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