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

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

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integral of cos^2(2u)

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

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

Solution steps

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

Rewrite using trig identities

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

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 u) d u

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 u + \int cos (4 u) d u)

\int 1 d u = u

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

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

Add a constant to the solution

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

\int x^{3} - 6 x^{2} + 8 x d x

x \to 0 lim (e^{3 x} - 1)

\int 4 x e^{- 2 x} d x

(x^{2} - 25 ln (x^{2}))^{^{'}}

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