What is the integral of cos(nwt) ?

The integral of cos(nwt) is 1/(wn)sin(nwt)+C

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integral of cos(nwt)

\int cos (n wt) d t

\frac{1}{w n} sin (n wt) + C

Solution steps

\int cos (n wt) d t

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = n wt

= \frac{1}{w n} sin (n wt)

Add a constant to the solution

= \frac{1}{w n} sin (n wt) + C