integral of (1/x+cot(x)-sec(x))

解

\int (\frac{1}{x} + cot (x) - sec (x)) d x

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

解答ステップ

\int \frac{1}{x} + cot (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 \frac{1}{x} d x + \int cot (x) d x - \int sec (x) d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int cot (x) d x = ln ∣ sin (x) ∣

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

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

定数を解答に追加する

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