integral of csc^6(x)

Lösung

\int csc^{6} (x) d x

- \frac{cos ( x ) csc ^{5} ( x )}{5} + \frac{4}{5} (- \frac{1}{3} csc^{3} (x) cos (x) - \frac{2}{3} cot (x)) + C

Schritte zur Lösung

\int csc^{6} (x) d x

Wende integrale Reduktion an

= - \frac{cos ( x ) csc ^{5} ( x )}{5} + \frac{4}{5} \cdot \int csc^{4} (x) d x

\int csc^{4} (x) d x = - \frac{1}{3} csc^{3} (x) cos (x) - \frac{2}{3} cot (x)

= - \frac{cos ( x ) csc ^{5} ( x )}{5} + \frac{4}{5} (- \frac{1}{3} csc^{3} (x) cos (x) - \frac{2}{3} cot (x))

Füge eine Konstante zur Lösung hinzu

= - \frac{cos ( x ) csc ^{5} ( x )}{5} + \frac{4}{5} (- \frac{1}{3} csc^{3} (x) cos (x) - \frac{2}{3} cot (x)) + C

t a y l or \frac{( 1 - v )}{( 1 + v )}

d er i v a t i v e f (x) = (0.001 + 2)^{0.001}

x \to \infty lim (e^{- 8 x^{2}})

\int \frac{( 2 x + 5 )}{x ^{2} + 5 x} d x

\frac{d}{d x} (\frac{csc ( x ) tan ( x )}{cos ( x )})