What is the integral of (1+cos(4x))/(1-cos(4x)) ?

The integral of (1+cos(4x))/(1-cos(4x)) is -1/2 cot(2x)-x+C

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integral of (1+cos(4x))/(1-cos(4x))

\int \frac{1 + cos ( 4 x )}{1 - cos ( 4 x )} d x

- \frac{1}{2} cot (2 x) - x + C

Solution steps

\int \frac{1 + cos ( 4 x )}{1 - cos ( 4 x )} d x

\frac{1 + cos ( 4 x )}{1 - cos ( 4 x )} = \frac{2}{1 - cos ( 4 x )} - 1

= \int \frac{2}{1 - cos ( 4 x )} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2}{1 - cos ( 4 x )} d x - \int 1 d x

\int \frac{2}{1 - cos ( 4 x )} d x = - \frac{1}{2} cot (2 x)

\int 1 d x = x

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

Add a constant to the solution

= - \frac{1}{2} cot (2 x) - x + C

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What is the integral of (1+cos(4x))/(1-cos(4x)) ?
The integral of (1+cos(4x))/(1-cos(4x)) is -1/2 cot(2x)-x+C