What is the integral of (sqrt(x))/(ln(x)) ?

The integral of (sqrt(x))/(ln(x)) is \Ei(3ln(sqrt(x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (sqrt(x))/(ln(x))

\int \frac{x}{ln ( x )} d x

Ei (3 ln (x)) + C

Solution steps

\int \frac{x}{ln ( x )} d x

Apply u-substitution

= \int \frac{u ^{2}}{ln ( u )} d u

Apply u-substitution

= \int \frac{e ^{3 v}}{v} d v

Apply u-substitution

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

Use the nonelementary integral:

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

= Ei (w)

Substitute back

= Ei (3 ln (x))

Add a constant to the solution

= Ei (3 ln (x)) + C

x \to - 2 lim (0)

\int x cos (2 - x^{2}) d x

n = 1 \sum \infty \frac{n}{11 n ^{2} + 1}

\frac{\partial}{\partial x} (z ln ∣ x ∣)

(6 y + 2 t - 7) d t + (4 y + 6 t - 1) d y = 0, y (- 1) = 2

What is the integral of (sqrt(x))/(ln(x)) ?
The integral of (sqrt(x))/(ln(x)) is \Ei(3ln(sqrt(x)))+C