integral of (sin(x)+7cos(x)-1)

解

\int (sin (x) + 7 cos (x) - 1) d x

- cos (x) + 7 sin (x) - x + C

解答ステップ

\int sin (x) + 7 cos (x) - 1 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 sin (x) d x + \int 7 cos (x) d x - \int 1 d x

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

\int 7 cos (x) d x = 7 sin (x)

\int 1 d x = x

= - cos (x) + 7 sin (x) - x

定数を解答に追加する

= - cos (x) + 7 sin (x) - x + C