What is the integral of e^{jwn} ?

The integral of e^{jwn} is 1/(jn)e^{jwn}+C

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integral of e^{jwn}

\int e^{j w n} d w

\frac{1}{jn} e^{j w n} + C

Solution steps

\int e^{j w n} d w

Apply u-substitution

= \int \frac{e ^{u}}{jn} d u

Take the constant out:

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

= \frac{1}{jn} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{jn} e^{u}

Substitute back

u = j w n

= \frac{1}{jn} e^{j w n}

Add a constant to the solution

= \frac{1}{jn} e^{j w n} + C