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

解

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

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

解答ステップ

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

総和規則を適用する:

\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

定数を解答に追加する

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