integral of xsin(3x)

Lösung

\int x sin (3 x) d x

- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x) + C

Schritte zur Lösung

\int x sin (3 x) d x

Wende die partielle Integration an

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

\int - \frac{1}{3} cos (3 x) d x = - \frac{1}{9} sin (3 x)

= - \frac{1}{3} x cos (3 x) - (- \frac{1}{9} sin (3 x))

Vereinfache

= - \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x) + C

a re a y = 2 cos (x), y = 6 - 4 cos (x), 0 \leq x \leq 2 π

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