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Popular >

integral of+e^{-jwt}

Solution

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

Solution

- \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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\int 5 x^{3} (x^{4} + 5)^{4} d x

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\int \frac{π}{2} cos (\frac{π x}{2}) d x

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\int \frac{7 x ^{5} - 8 x ^{2} + 1}{( x + 1 ) ( x ^{2} + 4 )} d x

Frequently Asked Questions (FAQ)

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