What is the integral of cos(2nt) ?

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

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integral of cos(2nt)

\int cos (2 n t) d t

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

Solution steps

\int cos (2 n t) d t

Apply u-substitution

= \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 t

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

Add a constant to the solution

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