What is the integral of (cos^3(y))/(1+cos(2y)) ?

The integral of (cos^3(y))/(1+cos(2y)) is 1/2 sin(y)+C

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integral of (cos^3(y))/(1+cos(2y))

\int \frac{cos ^{3} ( y )}{1 + cos ( 2 y )} d y

\frac{1}{2} sin (y) + C

Solution steps

\int \frac{cos ^{3} ( y )}{1 + cos ( 2 y )} d y

Rewrite using trig identities

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

Take the constant out:

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

= \frac{1}{2} \cdot \int cos (y) d y

Use the common integral:

\int cos (y) d y = sin (y)

= \frac{1}{2} sin (y)

Add a constant to the solution

= \frac{1}{2} sin (y) + C

What is the integral of (cos^3(y))/(1+cos(2y)) ?
The integral of (cos^3(y))/(1+cos(2y)) is 1/2 sin(y)+C