What is the integral of e^{jwt} ?

The integral of e^{jwt} is 1/(wj)e^{wjt}+C

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integral of e^{jwt}

\int e^{j wt} d t

\frac{1}{w j} e^{w j t} + C

Solution steps

\int e^{j wt} d t

Apply u-substitution

: \int \frac{e ^{u}}{w j} d u

= \int \frac{e ^{u}}{w j} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{w j} e^{u}

Substitute back

u = w j t

= \frac{1}{w j} e^{w j t}

Add a constant to the solution

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

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