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

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

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integral of cos^2(y)

\int cos^{2} (y) d y

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

Solution steps

\int cos^{2} (y) d y

Rewrite using trig identities

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

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

\int 1 d y = y

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

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{n}{5 ^{n}}

\frac{\partial}{\partial x} (x^{2} + x y - 10)

\frac{d}{d x} (2 x^{3} cos (x) sin (x))

n = 0 \sum \infty \frac{( - 1 ) ^{n}}{2}

t \to 0 lim (\frac{e ^{7 t} - 1}{sin ( t )})

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