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

解

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

- \frac{1}{2} ln ∣ cos (2 x) ∣ - \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣ + C

解答ステップ

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

\int tan (2 x) d x = - \frac{1}{2} ln ∣ cos (2 x) ∣

\int sec (2 x) d x = \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣

= - \frac{1}{2} ln ∣ cos (2 x) ∣ - \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣

定数を解答に追加する

= - \frac{1}{2} ln ∣ cos (2 x) ∣ - \frac{1}{2} ln ∣ tan (2 x) + sec (2 x) ∣ + C