What is the integral from 2 to 4 of 1/(ln(x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 4 of 1/(ln(x))

\int_{2}^{4} \frac{1}{ln ( x )} d x

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

Solution steps

\int_{2}^{4} \frac{1}{ln ( x )} d x

Apply u-substitution

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

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

Use the nonelementary integral:

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

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

Compute the boundaries:

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

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

\int_{1}^{b} 6 c x^{2} + 1 d x

\int_{1}^{3} x^{3} + 2 x d x

\int_{0.5}^{2.5} x d x

\int_{0}^{π} x^{2} \cdot sin (n x) d x

\int_{0}^{1} 4 x (1 - y) d x

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