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

The integral from 1 to x of (e^{xt})/t is \Ei(x^2)-\Ei(x)

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

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

Ei (x^{2}) - Ei (x)

Solution steps

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

Apply u-substitution

: \int_{x}^{x^{2}} \frac{e ^{u}}{u} d u

= \int_{x}^{x^{2}} \frac{e ^{u}}{u} d u

Use the nonelementary integral:

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

= [Ei (u)]_{x}^{x^{2}}

Compute the boundaries:

Ei (x^{2}) - Ei (x)

= Ei (x^{2}) - Ei (x)

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What is the integral from 1 to x of (e^{xt})/t ?
The integral from 1 to x of (e^{xt})/t is \Ei(x^2)-\Ei(x)