What is the integral of 1/((ln(x))^2) ?

The integral of 1/((ln(x))^2) is -x/(ln(x))+\Ei(ln(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((ln(x))^2)

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

- \frac{x}{ln ( x )} + Ei (ln (x)) + C

Solution steps

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

Simplify

= \int \frac{1}{ln ^{2} ( x )} d x

Apply u-substitution

: \int \frac{e ^{u}}{u ^{2}} d u

= \int \frac{e ^{u}}{u ^{2}} d u

Apply Integration By Parts

: - \frac{e ^{u}}{u} - \int - \frac{e ^{u}}{u} d u

= - \frac{e ^{u}}{u} - \int - \frac{e ^{u}}{u} d u

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

= - \frac{e ^{u}}{u} - (- Ei (u))

Substitute back

u = ln (x)

= - \frac{e ^{l n (x)}}{ln ( x )} - (- Ei (ln (x)))

Simplify

- \frac{e ^{l n (x)}}{ln ( x )} - (- Ei (ln (x))) : - \frac{x}{ln ( x )} + Ei (ln (x))

= - \frac{x}{ln ( x )} + Ei (ln (x))

Add a constant to the solution

= - \frac{x}{ln ( x )} + Ei (ln (x)) + C

\frac{\partial}{\partial y} (2 arctan (\frac{y}{x}))

f (x) = 2 + 3 x - 5 x^{2}, at x = 1

h \to 1 lim (4 h^{2} + x + 3)

\frac{d}{d x} (e^{x} sin (9 x))

e^{- 2 x} + \frac{1}{3} e^{x}

What is the integral of 1/((ln(x))^2) ?
The integral of 1/((ln(x))^2) is -x/(ln(x))+\Ei(ln(x))+C