integral of (2sin(x)-sec^2(x))

解

\int (2 sin (x) - sec^{2} (x)) d x

- 2 cos (x) - tan (x) + C

解答ステップ

\int 2 sin (x) - sec^{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 2 sin (x) d x - \int sec^{2} (x) d x

\int 2 sin (x) d x = - 2 cos (x)

\int sec^{2} (x) d x = tan (x)

= - 2 cos (x) - tan (x)

定数を解答に追加する

= - 2 cos (x) - tan (x) + C