What is the integral of 2/(e^{-t)} ?

The integral of 2/(e^{-t)} is 2e^t+C

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integral of 2/(e^{-t)}

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

2 e^{t} + C

Solution steps

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

Take the constant out:

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

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

Simplify

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

= 2 \cdot \int e^{t} d t

Use the common integral:

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

= 2 e^{t}

Add a constant to the solution

= 2 e^{t} + C