integral of x^2sin(yx)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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