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Beliebt Rechnen >

integral of (2x+1)sin(5x)

Lösung

\int (2 x + 1) sin (5 x) d x

Lösung

- \frac{1}{5} cos (5 x) (2 x + 1) + \frac{2}{25} sin (5 x) + C

Schritte zur Lösung

\int (2 x + 1) sin (5 x) d x

Wende die partielle Integration an

= - \frac{1}{5} cos (5 x) (2 x + 1) - \int - \frac{2}{5} cos (5 x) d x

\int - \frac{2}{5} cos (5 x) d x = - \frac{2}{25} sin (5 x)

= - \frac{1}{5} cos (5 x) (2 x + 1) - (- \frac{2}{25} sin (5 x))

Vereinfache

= - \frac{1}{5} cos (5 x) (2 x + 1) + \frac{2}{25} sin (5 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} cos (5 x) (2 x + 1) + \frac{2}{25} sin (5 x) + C

Graph

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