integral of (3sec(x)tan(x)-5csc^2(x))

解

\int (3 sec (x) tan (x) - 5 csc^{2} (x)) d x

3 sec (x) + 5 cot (x) + C

解答ステップ

\int 3 sec (x) tan (x) - 5 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 3 sec (x) tan (x) d x - \int 5 csc^{2} (x) d x

\int 3 sec (x) tan (x) d x = 3 sec (x)

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

= 3 sec (x) - (- 5 cot (x))

簡素化

= 3 sec (x) + 5 cot (x)

定数を解答に追加する

= 3 sec (x) + 5 cot (x) + C