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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 + tan (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 )} = tan^{2} (y)

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

Rewrite using trig identities

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

\int 1 d y = y

\int sec^{2} (y) d y = tan (y)

= - y + tan (y)

Add a constant to the solution

= - y + tan (y) + C

Popular Examples

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\int x arctan (7 x) d x

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\int (2 x^{2} + 3)^{2} \cdot 5 x d x

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\int \frac{1}{x 4 x ^{2} - 5} d x

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\int 4 1 - 25 x^{2} d x

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\int 5^{3 x + 2} + 4^{5 - x} d x

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+tan(y)+C