What is the integral of cos(2v) ?

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

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integral of cos(2v)

\int cos (2 v) d v

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

Solution steps

\int cos (2 v) d v

Apply u-substitution

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

Use the common integral:

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

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

Substitute back

u = 2 v

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

Add a constant to the solution

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