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

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

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integral of 4x^{1/3}+2x^{-2/3}+9

\int 4 x^{\frac{1}{3}} + 2 x^{- \frac{2}{3}} + 9 d x

3 x^{\frac{4}{3}} + 6 x^{\frac{1}{3}} + 9 x + C

Solution steps

\int 4 x^{\frac{1}{3}} + 2 x^{- \frac{2}{3}} + 9 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 2 x^{- \frac{2}{3}} d x + \int 9 d x

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

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

\int 9 d x = 9 x

= 3 x^{\frac{4}{3}} + 6 x^{\frac{1}{3}} + 9 x

Add a constant to the solution

= 3 x^{\frac{4}{3}} + 6 x^{\frac{1}{3}} + 9 x + C

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