integral of (5cos(x)+9sin(x))

解

\int (5 cos (x) + 9 sin (x)) d x

5 sin (x) - 9 cos (x) + C

解答ステップ

\int 5 cos (x) + 9 sin (x) 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 5 cos (x) d x + \int 9 sin (x) d x

\int 5 cos (x) d x = 5 sin (x)

\int 9 sin (x) d x = - 9 cos (x)

= 5 sin (x) - 9 cos (x)

定数を解答に追加する

= 5 sin (x) - 9 cos (x) + C