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

Lösung

\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

Schritte zur Lösung

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

Wende die partielle Integration an

= - \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) ∣)

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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