integral of (-2sec(x)tan(x)-3sec^2(x))

解

\int (- 2 sec (x) tan (x) - 3 sec^{2} (x)) d x

- 2 sec (x) - 3 tan (x) + C

解答ステップ

\int - 2 sec (x) tan (x) - 3 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 sec (x) tan (x) d x - \int 3 sec^{2} (x) d x

\int 2 sec (x) tan (x) d x = 2 sec (x)

\int 3 sec^{2} (x) d x = 3 tan (x)

= - 2 sec (x) - 3 tan (x)

定数を解答に追加する

= - 2 sec (x) - 3 tan (x) + C