integral of x^3sin(7x)

Lösung

\int x^{3} sin (7 x) d x

- \frac{1}{7} x^{3} cos (7 x) + \frac{3}{2401} (49 x^{2} sin (7 x) - 2 (- 7 x cos (7 x) + sin (7 x))) + C

Schritte zur Lösung

\int x^{3} sin (7 x) d x

Wende die partielle Integration an

= - \frac{1}{7} x^{3} cos (7 x) - \int - \frac{3}{7} x^{2} cos (7 x) d x

\int - \frac{3}{7} x^{2} cos (7 x) d x = - \frac{3}{2401} (49 x^{2} sin (7 x) - 2 (- 7 x cos (7 x) + sin (7 x)))

= - \frac{1}{7} x^{3} cos (7 x) - (- \frac{3}{2401} (49 x^{2} sin (7 x) - 2 (- 7 x cos (7 x) + sin (7 x))))

Vereinfache

= - \frac{1}{7} x^{3} cos (7 x) + \frac{3}{2401} (49 x^{2} sin (7 x) - 2 (- 7 x cos (7 x) + sin (7 x)))

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{7} x^{3} cos (7 x) + \frac{3}{2401} (49 x^{2} sin (7 x) - 2 (- 7 x cos (7 x) + sin (7 x))) + C

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