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Beliebt Rechnen >

integral of x^2sin(ax)

Lösung

\int x^{2} sin (a x) d x

Lösung

- \frac{1}{a} x^{2} cos (a x) + \frac{2}{a ^{3}} (a x sin (a x) + cos (a x)) + C

Schritte zur Lösung

\int x^{2} sin (a x) d x

Wende die partielle Integration an

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

\int - \frac{2}{a} x cos (a x) d x = - \frac{2}{a ^{3}} (a x sin (a x) + cos (a x))

= - \frac{1}{a} x^{2} cos (a x) - (- \frac{2}{a ^{3}} (a x sin (a x) + cos (a x)))

Vereinfache

= - \frac{1}{a} x^{2} cos (a x) + \frac{2}{a ^{3}} (a x sin (a x) + cos (a x))

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{a} x^{2} cos (a x) + \frac{2}{a ^{3}} (a x sin (a x) + cos (a x)) + C

Graph

Beliebte Beispiele

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