What is the integral of 1/(cos(2y)-cos^2(y)) ?

The integral of 1/(cos(2y)-cos^2(y)) is cot(y)+C

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

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

cot (y) + C

Solution steps

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

Rewrite using trig identities

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

Take the constant out:

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

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

Use the common integral:

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

= - (- cot (y))

Simplify

= cot (y)

Add a constant to the solution

= cot (y) + C

f (x) = (x - 2) (x^{2} + 4), (1, - 5)

sin (x), 0, π

3 e^{3 x}

4 y^{^{'''}} + 12 y^{^{''}} - 16 y^{^{'}} - 48 y = 0

f (x) = 8 x^{3} - 24 x^{2} - 193 x + 48

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