What is the integral of-e^{-jwt} ?

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

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integral of-e^{-jwt}

\int - e^{- j wt} d t

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

Solution steps

\int - e^{- j wt} d t

Take the constant out:

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

= - \int e^{- w j t} d t

Apply u-substitution

= - \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})

Simplify

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

Add a constant to the solution

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

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