What is the integral of (ln(x))/(x^{2/3)} ?

The integral of (ln(x))/(x^{2/3)} is 3x^{1/3}ln(x)-9x^{1/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (ln(x))/(x^{2/3)}

\int \frac{ln ( x )}{x ^{\frac{2}{3}}} d x

3 x^{\frac{1}{3}} ln (x) - 9 x^{\frac{1}{3}} + C

Solution steps

\int \frac{ln ( x )}{x ^{\frac{2}{3}}} d x

Apply Integration By Parts

: 3 x^{\frac{1}{3}} ln (x) - \int \frac{3}{x ^{\frac{2}{3}}} d x

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

\int \frac{3}{x ^{\frac{2}{3}}} d x = 9 x^{\frac{1}{3}}

= 3 x^{\frac{1}{3}} ln (x) - 9 x^{\frac{1}{3}}

Add a constant to the solution

= 3 x^{\frac{1}{3}} ln (x) - 9 x^{\frac{1}{3}} + C

\int sec (8 x + 5) tan (8 x + 5) d x

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

\int x (9 x^{2} + 5)^{3} d x

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

\int \frac{x + 1}{2 x} d x

What is the integral of (ln(x))/(x^{2/3)} ?
The integral of (ln(x))/(x^{2/3)} is 3x^{1/3}ln(x)-9x^{1/3}+C