integral of cot^7(x)

解

\int cot^{7} (x) d x

- \frac{1}{6} cot^{6} (x) + \frac{1}{4} cot^{4} (x) - \frac{1}{2} cot^{2} (x) - ln ∣ sin (x) ∣ + C

解答ステップ

\int cot^{7} (x) d x

積分換算を適用する

= - \frac{cot ^{6} ( x )}{6} - \int cot^{5} (x) d x

\int cot^{5} (x) d x = - \frac{1}{4} cot^{4} (x) + \frac{1}{2} cot^{2} (x) + ln ∣ sin (x) ∣

= - \frac{cot ^{6} ( x )}{6} - (- \frac{1}{4} cot^{4} (x) + \frac{1}{2} cot^{2} (x) + ln ∣ sin (x) ∣)

簡素化

- \frac{cot ^{6} ( x )}{6} - (- \frac{1}{4} cot^{4} (x) + \frac{1}{2} cot^{2} (x) + ln ∣ sin (x) ∣) : - \frac{1}{6} cot^{6} (x) + \frac{1}{4} cot^{4} (x) - \frac{1}{2} cot^{2} (x) - ln ∣ sin (x) ∣

= - \frac{1}{6} cot^{6} (x) + \frac{1}{4} cot^{4} (x) - \frac{1}{2} cot^{2} (x) - ln ∣ sin (x) ∣

定数を解答に追加する

= - \frac{1}{6} cot^{6} (x) + \frac{1}{4} cot^{4} (x) - \frac{1}{2} cot^{2} (x) - ln ∣ sin (x) ∣ + C