integral of (cos(x))/(sin^6(x))

解答

\int \frac{cos ( x )}{sin ^{6} ( x )} d x

- \frac{1}{5} csc^{5} (x) + C

求解步骤

\int \frac{cos ( x )}{sin ^{6} ( x )} d x

使用换元积分法

= \int \frac{1}{u ^{6}} d u

使用幂法则

= - \frac{1}{5 u ^{5}}

u = sin (x)

代回

= - \frac{1}{5 sin ^{5} ( x )}

化简

- \frac{1}{5 sin ^{5} ( x )} : - \frac{1}{5} csc^{5} (x)

= - \frac{1}{5} csc^{5} (x)

解答补常数

= - \frac{1}{5} csc^{5} (x) + C

\frac{d y}{d x} = \frac{x}{18 y}

(2 x + t) \frac{d x}{d t} + (x - 2 t) = 0

f (x) = sin^{5} (2 x) cos^{3} (2 x)

(x^{2} - 1) y^{^{'}} = 2 y

t an g e n t y = \frac{x ^{2} + 1}{3 x + 1}, at x = 0