integral of 1/(sin(x))(cos(x))/(sin(x))

解答

\int \frac{1}{sin ( x )} \frac{cos ( x )}{sin ( x )} d x

- csc (x) + C

求解步骤

\int \frac{1}{sin ( x )} \cdot \frac{cos ( x )}{sin ( x )} d x

化简

\frac{1}{sin ( x )} \cdot \frac{cos ( x )}{sin ( x )} : cot (x) csc (x)

= \int cot (x) csc (x) d x

使用换元积分法

= \int - 1 d u

常数积分:

\int a d x = a x

= (- 1) u

u = csc (x)

代回

= (- 1) csc (x)

化简

= - csc (x)

解答补常数

= - csc (x) + C

h \to 0 lim (\frac{( 1 + h ) 3 - 1}{h})

x, y \to (0, 0) lim (\frac{( 2 x ^{2} y )}{x ^{2} + y ^{4}})

x \to 2 + lim (3 - x)

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

y^{^{''}} + 2 y^{^{'}} + y = 64 e^{(7 t)}