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Beliebt Rechnen >

integral 4cos^2(x)-2sin^2(x)

Lösung

integral

4 cos^{2} (x) - 2 sin^{2} (x)

Lösung

x + \frac{3}{2} sin (2 x) + C

Schritte zur Lösung

\int 4 cos^{2} (x) - 2 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 4 cos^{2} (x) d x - \int 2 sin^{2} (x) d x

\int 4 cos^{2} (x) d x = 2 x + sin (2 x)

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

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

Vereinfache

2 x + sin (2 x) - (x - \frac{1}{2} sin (2 x)) : x + \frac{3}{2} sin (2 x)

= x + \frac{3}{2} sin (2 x)

Füge eine Konstante zur Lösung hinzu

= x + \frac{3}{2} sin (2 x) + C

Graph

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