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

解

\int cos (x) sec (s - π) d s

cos (x) (s sec (s - π) + s sec (s) - ln ∣ tan (s) + sec (s) ∣) + C

解答ステップ

\int cos (x) sec (s - π) d s

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos (x) \cdot \int sec (s - π) d s

部分積分を適用する

= cos (x) (s sec (s - π) - \int - s sec (s) tan (s) d s)

\int - s sec (s) tan (s) d s = - s sec (s) + ln ∣ tan (s) + sec (s) ∣

= cos (x) (s sec (s - π) - (- s sec (s) + ln ∣ tan (s) + sec (s) ∣))

簡素化

= cos (x) (s sec (s - π) + s sec (s) - ln ∣ tan (s) + sec (s) ∣)

定数を解答に追加する

= cos (x) (s sec (s - π) + s sec (s) - ln ∣ tan (s) + sec (s) ∣) + C