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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

l a pl a ce t r an s f or m t \cdot sin (k \cdot t)

x \to - 4 lim (- 5 x - 8)

x y^{^{'}} - 2 y = x^{2} - x - 2

y^{^{'}} = x e^{y - x^{2}}

a re a x = 2 y^{2}, x = 2