What is the integral of (14)/(1-cos(2x)) ?

The integral of (14)/(1-cos(2x)) is -7cot(x)+C

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

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

- 7 cot (x) + C

Solution steps

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

Take the constant out:

\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

Rewrite using trig identities

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

Take the constant out:

\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

Use the common integral:

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

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

Simplify

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

= - 7 cot (x)

Add a constant to the solution

= - 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})

f (x) = sin (x), (0, 0)

What is the integral of (14)/(1-cos(2x)) ?
The integral of (14)/(1-cos(2x)) is -7cot(x)+C