What is the integral of 1/(e^{-t)} ?

The integral of 1/(e^{-t)} is e^t+C

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integral of 1/(e^{-t)}

\int \frac{1}{e ^{- t}} d t

e^{t} + C

Solution steps

\int \frac{1}{e ^{- t}} d t

Simplify

\frac{1}{e ^{- t}} : e^{t}

= \int e^{t} d t

Use the common integral:

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

= e^{t}

Add a constant to the solution

= e^{t} + C

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