integral of (14)/(1-cos(2x))

解答

\int \frac{14}{1 - cos ( 2 x )} d x

- 7 cot (x) + C

求解步骤

\int \frac{14}{1 - cos ( 2 x )} d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 14 \cdot \int \frac{1}{1 - cos ( 2 x )} d x

使用三角恒等式改写

= 14 \cdot \int \frac{1}{2 sin ^{2} ( x )} d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 14 \cdot \frac{1}{2} \cdot \int \frac{1}{sin ^{2} ( x )} d x

使用积分常见定则:

\int \frac{1}{sin ^{2} ( x )} d x = - cot (x)

= 14 \cdot \frac{1}{2} (- cot (x))

化简

14 \cdot \frac{1}{2} (- cot (x)) : - 7 cot (x)

= - 7 cot (x)

解答补常数

= - 7 cot (x) + C

\int 6 x^{2} y - 2 x d y

\frac{\partial}{\partial x} (y x^{2} + x y^{2} + y z^{2})

\int \frac{e ^{x} ( 1 + x )}{cos ^{2} ( x e ^{x} )} d x

\frac{d}{d x} (\frac{x}{8} - \frac{8}{x})

t an g e n t f (x) = sin (x), (0, 0)