integral of (cos(x)-sec(x))

解

\int (cos (x) - sec (x)) d x

sin (x) - ln ∣ tan (x) + sec (x) ∣ + C

解答ステップ

\int cos (x) - sec (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 cos (x) d x - \int sec (x) d x

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

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= sin (x) - ln ∣ tan (x) + sec (x) ∣

定数を解答に追加する

= sin (x) - ln ∣ tan (x) + sec (x) ∣ + C