What is the integral of e^{-2at} ?

The integral of e^{-2at} is -1/(2a)e^{-2at}+C

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integral of e^{-2at}

\int e^{- 2 a t} d t

- \frac{1}{2 a} e^{- 2 a t} + C

Solution steps

\int e^{- 2 a t} d t

Apply u-substitution

: \int - \frac{e ^{u}}{2 a} d u

= \int - \frac{e ^{u}}{2 a} d u

Take the constant out:

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

= - \frac{1}{2 a} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{2 a} e^{u}

Substitute back

u = - 2 a t

= - \frac{1}{2 a} e^{- 2 a t}

Add a constant to the solution

= - \frac{1}{2 a} e^{- 2 a t} + C

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What is the integral of e^{-2at} ?
The integral of e^{-2at} is -1/(2a)e^{-2at}+C