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Beliebt Rechnen >

integral of (-6x^2+4x-4xcos(x))

Lösung

\int (- 6 x^{2} + 4 x - 4 x cos (x)) d x

Lösung

- 2 x^{3} + 2 x^{2} - 4 (x sin (x) + cos (x)) + C

Schritte zur Lösung

\int - 6 x^{2} + 4 x - 4 x cos (x) 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 6 x^{2} d x + \int 4 x d x - \int 4 x cos (x) d x

\int 6 x^{2} d x = 2 x^{3}

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

\int 4 x cos (x) d x = 4 (x sin (x) + cos (x))

= - 2 x^{3} + 2 x^{2} - 4 (x sin (x) + cos (x))

Füge eine Konstante zur Lösung hinzu

= - 2 x^{3} + 2 x^{2} - 4 (x sin (x) + cos (x)) + C

Graph

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