integral of 5cos(x)-csc^2(x)

解

\int 5 cos (x) - csc^{2} (x) d x

5 sin (x) + cot (x) + C

解答ステップ

\int 5 cos (x) - csc^{2} (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 csc^{2} (x) d x

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

\int csc^{2} (x) d x = - cot (x)

= 5 sin (x) - (- cot (x))

簡素化

= 5 sin (x) + cot (x)

定数を解答に追加する

= 5 sin (x) + cot (x) + C