integral of xsin(cx)

Lösung

\int x sin (c x) d x

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

Schritte zur Lösung

\int x sin (c x) d x

Wende die partielle Integration an

= - \frac{1}{c} x cos (c x) - \int - \frac{1}{c} cos (c x) d x

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

= - \frac{1}{c} x cos (c x) - (- \frac{1}{c ^{2}} sin (c x))

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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