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

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

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

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

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

Solution steps

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

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

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

= 3 x^{\frac{4}{3}} + 3 x^{\frac{2}{3}}

Add a constant to the solution

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

y^{^{'}} = y (x y^{6} + 3)

2 x^{^{''}} + 40 x = 0

\frac{x - 5}{x + 5}

f (t) = (1 + e^{2 t})^{2}

\frac{d}{d x} (4 - 6 x)

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