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Beliebt Rechnen >

integral of 2xcos(x)-x^2sin(x)

Lösung

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

Lösung

x^{2} cos (x) + C

Schritte zur Lösung

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

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

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

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

Vereinfache

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

= x^{2} cos (x)

Füge eine Konstante zur Lösung hinzu

= x^{2} cos (x) + C

Graph

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