integral of x^2sin(5x)

Lösung

\int x^{2} sin (5 x) d x

- \frac{1}{5} x^{2} cos (5 x) + \frac{2}{125} (5 x sin (5 x) + cos (5 x)) + C

Schritte zur Lösung

\int x^{2} sin (5 x) d x

Wende die partielle Integration an

= - \frac{1}{5} x^{2} cos (5 x) - \int - \frac{2}{5} x cos (5 x) d x

\int - \frac{2}{5} x cos (5 x) d x = - \frac{2}{125} (5 x sin (5 x) + cos (5 x))

= - \frac{1}{5} x^{2} cos (5 x) - (- \frac{2}{125} (5 x sin (5 x) + cos (5 x)))

Vereinfache

= - \frac{1}{5} x^{2} cos (5 x) + \frac{2}{125} (5 x sin (5 x) + cos (5 x))

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} x^{2} cos (5 x) + \frac{2}{125} (5 x sin (5 x) + cos (5 x)) + C

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