integral of x^2csc^2(x)cot(x)

解

\int x^{2} csc^{2} (x) cot (x) d x

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

解答ステップ

\int x^{2} csc^{2} (x) cot (x) d x

部分積分を適用する

= - \frac{1}{2} x^{2} csc^{2} (x) - \int - x csc^{2} (x) d x

\int - x csc^{2} (x) d x = x cot (x) - ln ∣ sin (x) ∣

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

簡素化

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

定数を解答に追加する

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