integral of (cot^2(x)+cot^4(x))

解

\int (cot^{2} (x) + cot^{4} (x)) d x

- \frac{1}{3} cot^{3} (x) + C

解答ステップ

\int cot^{2} (x) + cot^{4} (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 cot^{2} (x) d x + \int cot^{4} (x) d x

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

\int cot^{4} (x) d x = - \frac{1}{3} cot^{3} (x) + x + cot (x)

= - x - cot (x) - \frac{1}{3} cot^{3} (x) + x + cot (x)

簡素化

= - \frac{1}{3} cot^{3} (x)

定数を解答に追加する

= - \frac{1}{3} cot^{3} (x) + C