integral of csc^9(x)

Lösung

\int csc^{9} (x) d x

- \frac{cos ( x ) csc ^{8} ( x )}{8} + \frac{7}{8} (- \frac{1}{6} csc^{6} (x) cos (x) + \frac{5}{48} (- 2 csc^{4} (x) cos (x) + 3 (- cot (x) csc (x) + ln tan (\frac{x}{2})))) + C

Schritte zur Lösung

\int csc^{9} (x) d x

Wende integrale Reduktion an

= - \frac{cos ( x ) csc ^{8} ( x )}{8} + \frac{7}{8} \cdot \int csc^{7} (x) d x

\int csc^{7} (x) d x = - \frac{1}{6} csc^{6} (x) cos (x) + \frac{5}{48} (- 2 csc^{4} (x) cos (x) + 3 (- cot (x) csc (x) + ln tan (\frac{x}{2})))

= - \frac{cos ( x ) csc ^{8} ( x )}{8} + \frac{7}{8} (- \frac{1}{6} csc^{6} (x) cos (x) + \frac{5}{48} (- 2 csc^{4} (x) cos (x) + 3 (- cot (x) csc (x) + ln tan (\frac{x}{2}))))

Füge eine Konstante zur Lösung hinzu

= - \frac{cos ( x ) csc ^{8} ( x )}{8} + \frac{7}{8} (- \frac{1}{6} csc^{6} (x) cos (x) + \frac{5}{48} (- 2 csc^{4} (x) cos (x) + 3 (- cot (x) csc (x) + ln tan (\frac{x}{2})))) + C

x \to 0 lim (x^{2} - 3 x + 3)

\frac{d}{d x} (\frac{2 x}{x})

x \to 0 + lim (\frac{3}{x})

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