integral of 1/2 sin(2x)-cos(x)+C

Lösung

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

- \frac{1}{4} cos (2 x) - sin (x) + C x + C

Schritte zur Lösung

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

\int \frac{1}{2} sin (2 x) d x = - \frac{1}{4} cos (2 x)

\int cos (x) d x = sin (x)

\int C d x = C x

= - \frac{1}{4} cos (2 x) - sin (x) + C x

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4} cos (2 x) - sin (x) + C x + C

z \to - 2 lim (z^{3} + 8)

t an g e n t f (x) = \frac{8}{x}, at x = 25

x \to 0 lim (1 - 1 + x)

\int_{1}^{3} \frac{5}{x ^{2} + 4 x + 4} d x

\frac{d}{d x} (3 x^{2} e^{x} + e^{x} (x^{3} + 8))