What is the integral from 1 to x of (e^t)/t ?

The integral from 1 to x of (e^t)/t is \Ei(x)-\Ei(1)

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integral from 1 to x of (e^t)/t

\int_{1}^{x} \frac{e ^{t}}{t} d t

Ei (x) - Ei (1)

Solution steps

\int_{1}^{x} \frac{e ^{t}}{t} d t

Use the nonelementary integral:

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

= [Ei (t)]_{1}^{x}

Compute the boundaries:

Ei (x) - Ei (1)

= Ei (x) - Ei (1)

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What is the integral from 1 to x of (e^t)/t ?
The integral from 1 to x of (e^t)/t is \Ei(x)-\Ei(1)