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

解

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

tan (x) - sec (x) + C

解答ステップ

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

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

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

= tan (x) - sec (x)

定数を解答に追加する

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