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

The integral of cos^2(2y) is 1/2 (y+1/4 sin(4y))+C

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integral of cos^2(2y)

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

\frac{1}{2} (y + \frac{1}{4} sin (4 y)) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1}{2} (1 + cos (4 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 1 + cos (4 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 (4 y) d y)

\int 1 d y = y

\int cos (4 y) d y = \frac{1}{4} sin (4 y)

= \frac{1}{2} (y + \frac{1}{4} sin (4 y))

Add a constant to the solution

= \frac{1}{2} (y + \frac{1}{4} sin (4 y)) + C

e^{t^{2}}

\int \frac{1}{x x ^{2} + 49} d x

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\int \frac{1}{30} e^{- \frac{x}{30}} d x

What is the integral of cos^2(2y) ?
The integral of cos^2(2y) is 1/2 (y+1/4 sin(4y))+C