integral of [(tan(x))^2+(cot(x))^2]

解

\int [(tan (x))^{2} + (cot (x))^{2}] d x

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

解答ステップ

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

簡素化

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

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

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

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

簡素化

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

定数を解答に追加する

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