What is the integral of 2x^{-2/3}-2x^{5/3} ?

The integral of 2x^{-2/3}-2x^{5/3} is 6x^{1/3}-3/4 x^{8/3}+C

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integral of 2x^{-2/3}-2x^{5/3}

\int 2 x^{- \frac{2}{3}} - 2 x^{\frac{5}{3}} d x

6 x^{\frac{1}{3}} - \frac{3}{4} x^{\frac{8}{3}} + C

Solution steps

\int 2 x^{- \frac{2}{3}} - 2 x^{\frac{5}{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 2 x^{- \frac{2}{3}} d x - \int 2 x^{\frac{5}{3}} d x

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

\int 2 x^{\frac{5}{3}} d x = \frac{3}{4} x^{\frac{8}{3}}

= 6 x^{\frac{1}{3}} - \frac{3}{4} x^{\frac{8}{3}}

Add a constant to the solution

= 6 x^{\frac{1}{3}} - \frac{3}{4} x^{\frac{8}{3}} + C

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What is the integral of 2x^{-2/3}-2x^{5/3} ?
The integral of 2x^{-2/3}-2x^{5/3} is 6x^{1/3}-3/4 x^{8/3}+C