What is the integral of cos(2nx) ?

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

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integral of cos(2nx)

\int cos (2 n x) d x

\frac{1}{2 n} sin (2 n x) + C

Solution steps

\int cos (2 n x) d x

Apply u-substitution

: \int \frac{cos ( u )}{2 n} d u

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = 2 n x

= \frac{1}{2 n} sin (2 n x)

Add a constant to the solution

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

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