integral of csc^{13}(x)

解答

\int csc^{13} (x) d x

- \frac{cos ( x ) csc ^{12} ( x )}{12} + \frac{11}{12} (- \frac{1}{10} csc^{10} (x) cos (x) + \frac{3}{1280} (7 (5 (3 (ln tan (\frac{x}{2}) - cot (x) csc (x)) - 2 csc^{4} (x) cos (x)) - 8 csc^{6} (x) cos (x)) - 48 csc^{8} (x) cos (x))) + C

求解步骤

\int csc^{13} (x) d x

使用降次积分法

= - \frac{cos ( x ) csc ^{12} ( x )}{12} + \frac{11}{12} \cdot \int csc^{11} (x) d x

\int csc^{11} (x) d x = - \frac{1}{10} csc^{10} (x) cos (x) + \frac{3}{1280} (7 (5 (3 (ln tan (\frac{x}{2}) - cot (x) csc (x)) - 2 csc^{4} (x) cos (x)) - 8 csc^{6} (x) cos (x)) - 48 csc^{8} (x) cos (x))

= - \frac{cos ( x ) csc ^{12} ( x )}{12} + \frac{11}{12} (- \frac{1}{10} csc^{10} (x) cos (x) + \frac{3}{1280} (7 (5 (3 (ln tan (\frac{x}{2}) - cot (x) csc (x)) - 2 csc^{4} (x) cos (x)) - 8 csc^{6} (x) cos (x)) - 48 csc^{8} (x) cos (x)))

解答补常数

= - \frac{cos ( x ) csc ^{12} ( x )}{12} + \frac{11}{12} (- \frac{1}{10} csc^{10} (x) cos (x) + \frac{3}{1280} (7 (5 (3 (ln tan (\frac{x}{2}) - cot (x) csc (x)) - 2 csc^{4} (x) cos (x)) - 8 csc^{6} (x) cos (x)) - 48 csc^{8} (x) cos (x))) + C

a re a g (x) = \frac{4}{2 - x}, y = 4, x = 0

\frac{\partial}{\partial x} (x + y^{4})

\frac{d}{d x} ((2 x^{3} + 3 x - 1)^{4})

\frac{\partial}{\partial x} (3 x^{3} y^{3} - 2 x^{2} + 3 y + 40)

s l o p e 2 - \frac{4}{t}