What is the integral from 4 to 7 of 1/(ln(x)) ?

The integral from 4 to 7 of 1/(ln(x)) is \Ei(ln(7))-\Ei(2ln(2))

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integral from 4 to 7 of 1/(ln(x))

\int_{4}^{7} \frac{1}{ln ( x )} d x

Ei (ln (7)) - Ei (2 ln (2))

Solution steps

\int_{4}^{7} \frac{1}{ln ( x )} d x

Apply u-substitution

: \int_{2 l n (2)}^{l n (7)} \frac{e ^{u}}{u} d u

= \int_{2 l n (2)}^{l n (7)} \frac{e ^{u}}{u} d u

Use the nonelementary integral:

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

= [Ei (u)]_{2 l n (2)}^{l n (7)}

Compute the boundaries:

Ei (ln (7)) - Ei (2 ln (2))

= Ei (ln (7)) - Ei (2 ln (2))

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What is the integral from 4 to 7 of 1/(ln(x)) ?
The integral from 4 to 7 of 1/(ln(x)) is \Ei(ln(7))-\Ei(2ln(2))