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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{2} x^{2} sin (2 x) + \frac{1}{2} x cos (2 x) - \frac{5}{4} sin (2 x) + C

Schritte zur Lösung

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

Multipliziere aus

(x^{2} - 2) cos (2 x) : x^{2} cos (2 x) - 2 cos (2 x)

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

\int x^{2} cos (2 x) d x = \frac{1}{2} x^{2} sin (2 x) + \frac{1}{2} x cos (2 x) - \frac{1}{4} sin (2 x)

\int 2 cos (2 x) d x = sin (2 x)

= \frac{1}{2} x^{2} sin (2 x) + \frac{1}{2} x cos (2 x) - \frac{1}{4} sin (2 x) - sin (2 x)

Addiere gleiche Elemente:

- \frac{1}{4} sin (2 x) - sin (2 x) = - \frac{5}{4} sin (2 x)

= \frac{1}{2} x^{2} sin (2 x) + \frac{1}{2} x cos (2 x) - \frac{5}{4} sin (2 x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} sin (2 x) + \frac{1}{2} x cos (2 x) - \frac{5}{4} sin (2 x) + C

Graph

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