What is the integral of sin(nwt) ?

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

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integral of sin(nwt)

\int sin (n wt) d t

- \frac{1}{w n} cos (w n t) + C

Solution steps

\int sin (n wt) d t

Apply u-substitution

: \int \frac{sin ( u )}{w n} d u

= \int \frac{sin ( 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 sin (u) d u

Use the common integral:

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

= \frac{1}{w n} (- cos (u))

Substitute back

u = w n t

= \frac{1}{w n} (- cos (w n t))

Simplify

= - \frac{1}{w n} cos (w n t)

Add a constant to the solution

= - \frac{1}{w n} cos (w n t) + C

\int sin (23 x) d x

\int \frac{x}{1 + x - 1} d x

f (x) = arctan (x)

\int (1 + x^{2}) \cdot sin (2 x) d x

What is the integral of sin(nwt) ?
The integral of sin(nwt) is -1/(wn)cos(wnt)+C