What is the integral of 1/(x*(ln(x))^3) ?

The integral of 1/(x*(ln(x))^3) is -1/(2ln^2(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/(x*(ln(x))^3)

\int \frac{1}{x \cdot ( ln ( x ) ) ^{3}} d x

- \frac{1}{2 ln ^{2} ( x )} + C

Solution steps

\int \frac{1}{x ( ln ( x ) ) ^{3}} d x

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= - \frac{1}{2 u ^{2}}

Substitute back

u = ln (x)

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

Add a constant to the solution

= - \frac{1}{2 ln ^{2} ( x )} + C

\int (\frac{1}{x ^{2}} + \frac{2}{x ^{3}} + \frac{3}{x ^{4}}) d x

\int 100 x e^{x^{2}} d x

\int a tan (x) d x

\int tan (θ) ln (cos (θ)) d θ

\int e^{- 0.005 x} d x

What is the integral of 1/(x*(ln(x))^3) ?
The integral of 1/(x*(ln(x))^3) is -1/(2ln^2(x))+C