integral of xsin(2x+1)

Lösung

\int x sin (2 x + 1) d x

- \frac{1}{2} x cos (2 x + 1) + \frac{1}{4} sin (2 x + 1) + C

Schritte zur Lösung

\int x sin (2 x + 1) d x

Wende die partielle Integration an

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

\int - \frac{1}{2} cos (2 x + 1) d x = - \frac{1}{4} sin (2 x + 1)

= - \frac{1}{2} x cos (2 x + 1) - (- \frac{1}{4} sin (2 x + 1))

Vereinfache

= - \frac{1}{2} x cos (2 x + 1) + \frac{1}{4} sin (2 x + 1)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} x cos (2 x + 1) + \frac{1}{4} sin (2 x + 1) + C

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