integral of xsin(1+5x)

Lösung

\int x sin (1 + 5 x) d x

- \frac{1}{5} x cos (1 + 5 x) + \frac{1}{25} sin (1 + 5 x) + C

Schritte zur Lösung

\int x sin (1 + 5 x) d x

Wende die partielle Integration an

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

\int - \frac{1}{5} cos (1 + 5 x) d x = - \frac{1}{25} sin (1 + 5 x)

= - \frac{1}{5} x cos (1 + 5 x) - (- \frac{1}{25} sin (1 + 5 x))

Vereinfache

= - \frac{1}{5} x cos (1 + 5 x) + \frac{1}{25} sin (1 + 5 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} x cos (1 + 5 x) + \frac{1}{25} sin (1 + 5 x) + C

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