integral of xcos(3x+2)

Lösung

\int x cos (3 x + 2) d x

\frac{1}{3} x sin (3 x + 2) + \frac{1}{9} cos (3 x + 2) + C

Schritte zur Lösung

\int x cos (3 x + 2) d x

Wende die partielle Integration an

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

\int \frac{1}{3} sin (3 x + 2) d x = - \frac{1}{9} cos (3 x + 2)

= \frac{1}{3} x sin (3 x + 2) - (- \frac{1}{9} cos (3 x + 2))

Vereinfache

= \frac{1}{3} x sin (3 x + 2) + \frac{1}{9} cos (3 x + 2)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x sin (3 x + 2) + \frac{1}{9} cos (3 x + 2) + C

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