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Beliebt Rechnen >

integral of (sin(3x)+cos(5x)-sin(x/2))

Lösung

\int (sin (3 x) + cos (5 x) - sin (\frac{x}{2})) d x

Lösung

- \frac{1}{3} cos (3 x) + \frac{1}{5} sin (5 x) + 2 cos (\frac{x}{2}) + C

Schritte zur Lösung

\int sin (3 x) + cos (5 x) - sin (\frac{x}{2}) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sin (3 x) d x + \int cos (5 x) d x - \int sin (\frac{x}{2}) d x

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

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

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

= - \frac{1}{3} cos (3 x) + \frac{1}{5} sin (5 x) - (- 2 cos (\frac{x}{2}))

Vereinfache

= - \frac{1}{3} cos (3 x) + \frac{1}{5} sin (5 x) + 2 cos (\frac{x}{2})

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{3} cos (3 x) + \frac{1}{5} sin (5 x) + 2 cos (\frac{x}{2}) + C

Graph

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