What is the integral of 4x^{1/3}-6x^{-1/3} ?

The integral of 4x^{1/3}-6x^{-1/3} is 3x^{4/3}-9x^{2/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 4x^{1/3}-6x^{-1/3}

\int 4 x^{\frac{1}{3}} - 6 x^{- \frac{1}{3}} d x

3 x^{\frac{4}{3}} - 9 x^{\frac{2}{3}} + C

Solution steps

\int 4 x^{\frac{1}{3}} - 6 x^{- \frac{1}{3}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 x^{\frac{1}{3}} d x - \int 6 x^{- \frac{1}{3}} d x

\int 4 x^{\frac{1}{3}} d x = 3 x^{\frac{4}{3}}

\int 6 x^{- \frac{1}{3}} d x = 9 x^{\frac{2}{3}}

= 3 x^{\frac{4}{3}} - 9 x^{\frac{2}{3}}

Add a constant to the solution

= 3 x^{\frac{4}{3}} - 9 x^{\frac{2}{3}} + C

What is the integral of 4x^{1/3}-6x^{-1/3} ?
The integral of 4x^{1/3}-6x^{-1/3} is 3x^{4/3}-9x^{2/3}+C