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Popular >

integral of (1+cos(2y))/(1-cos(2y))

Solution

\int \frac{1 + cos ( 2 y )}{1 - cos ( 2 y )} d y

Solution

- y - cot (y) + C

Solution steps

\int \frac{1 + cos ( 2 y )}{1 - cos ( 2 y )} d y

\frac{1 + cos ( 2 y )}{1 - cos ( 2 y )} = cot^{2} (y)

= \int cot^{2} (y) d y

Rewrite using trig identities

= \int - 1 + csc^{2} (y) d y

Apply the Sum Rule:

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

= - \int 1 d y + \int csc^{2} (y) d y

\int 1 d y = y

\int csc^{2} (y) d y = - cot (y)

= - y - cot (y)

Add a constant to the solution

= - y - cot (y) + C

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Frequently Asked Questions (FAQ)

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