integral of (cos(2x)-sin(2x))

Lösung

\int (cos (2 x) - sin (2 x)) d x

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

Schritte zur Lösung

\int cos (2 x) - sin (2 x) 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 cos (2 x) d x - \int sin (2 x) d x

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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