integral of (2cot^2(x)-3tan^2(x))

解

\int (2 cot^{2} (x) - 3 tan^{2} (x)) d x

x - 2 cot (x) - 3 tan (x) + C

解答ステップ

\int 2 cot^{2} (x) - 3 tan^{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 2 cot^{2} (x) d x - \int 3 tan^{2} (x) d x

\int 2 cot^{2} (x) d x = 2 (- x - cot (x))

\int 3 tan^{2} (x) d x = 3 (- x + tan (x))

= 2 (- x - cot (x)) - 3 (- x + tan (x))

簡素化

2 (- x - cot (x)) - 3 (- x + tan (x)) : x - 2 cot (x) - 3 tan (x)

= x - 2 cot (x) - 3 tan (x)

定数を解答に追加する

= x - 2 cot (x) - 3 tan (x) + C