What is the integral of cos(2u) ?

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

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integral of cos(2u)

\int cos (2 u) d u

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

Solution steps

\int cos (2 u) d u

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

v = 2 u

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

Add a constant to the solution

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