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Beliebt Rechnen >

integral of (x^2-1)sin(x)

Lösung

\int (x^{2} - 1) sin (x) d x

Lösung

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

Schritte zur Lösung

\int (x^{2} - 1) sin (x) d x

Wende die partielle Integration an

= - cos (x) (x^{2} - 1) - \int - 2 x cos (x) d x

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

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

Vereinfache

- cos (x) (x^{2} - 1) - (- 2 (x sin (x) + cos (x))) : - x^{2} cos (x) + 2 x sin (x) + 3 cos (x)

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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