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

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

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

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

Ei (- t) + C

Solution steps

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

Apply u-substitution

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

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= Ei (u)

Substitute back

u = - t

= Ei (- t)

Add a constant to the solution

= Ei (- t) + C