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

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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