What is the integral of 1/(x\sqrt[3]{ln(x)-1)} ?

The integral of 1/(x\sqrt[3]{ln(x)-1)} is 3/2 (ln(x)-1)^{2/3}+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\sqrt[3]{ln(x)-1)}

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

\frac{3}{2} (ln (x) - 1)^{\frac{2}{3}} + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: \frac{3}{2} u^{\frac{2}{3}}

= \frac{3}{2} u^{\frac{2}{3}}

Substitute back

u = ln (x) - 1

= \frac{3}{2} (ln (x) - 1)^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{2} (ln (x) - 1)^{\frac{2}{3}} + C

\int_{- 2}^{1} (- 2 x + 3) d x

\int \frac{1}{4 y ^{3}} d y

\int 2 x + 6 cos (x) d x

\int \frac{x ^{2}}{3 x + 2} d x

\int - \frac{2}{81 - 49 t ^{2}} d t

What is the integral of 1/(x\sqrt[3]{ln(x)-1)} ?
The integral of 1/(x\sqrt[3]{ln(x)-1)} is 3/2 (ln(x)-1)^{2/3}+C