integral of x^3cos(7x)

Lösung

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

\frac{1}{7} x^{3} sin (7 x) - \frac{3}{7} (- \frac{1}{7} x^{2} cos (7 x) + \frac{2}{343} (7 x sin (7 x) + cos (7 x))) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{3}{7} x^{2} sin (7 x) d x = \frac{3}{7} (- \frac{1}{7} x^{2} cos (7 x) + \frac{2}{343} (7 x sin (7 x) + cos (7 x)))

= \frac{1}{7} x^{3} sin (7 x) - \frac{3}{7} (- \frac{1}{7} x^{2} cos (7 x) + \frac{2}{343} (7 x sin (7 x) + cos (7 x)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{7} x^{3} sin (7 x) - \frac{3}{7} (- \frac{1}{7} x^{2} cos (7 x) + \frac{2}{343} (7 x sin (7 x) + cos (7 x))) + C

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