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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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