What is the integral of 8x^{1/3}+8x^{-1/3} ?

The integral of 8x^{1/3}+8x^{-1/3} is 6x^{4/3}+12x^{2/3}+C

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integral of 8x^{1/3}+8x^{-1/3}

\int 8 x^{\frac{1}{3}} + 8 x^{- \frac{1}{3}} d x

6 x^{\frac{4}{3}} + 12 x^{\frac{2}{3}} + C

Solution steps

\int 8 x^{\frac{1}{3}} + 8 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 8 x^{\frac{1}{3}} d x + \int 8 x^{- \frac{1}{3}} d x

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

\int 8 x^{- \frac{1}{3}} d x = 12 x^{\frac{2}{3}}

= 6 x^{\frac{4}{3}} + 12 x^{\frac{2}{3}}

Add a constant to the solution

= 6 x^{\frac{4}{3}} + 12 x^{\frac{2}{3}} + C

\int_{0}^{2} ln (2 x) d x

\frac{\partial}{\partial x} (\frac{y}{ln ( x - 1 )})

\frac{d y}{d t} + a y = 0

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

\frac{\partial}{\partial z} (2 x)

What is the integral of 8x^{1/3}+8x^{-1/3} ?
The integral of 8x^{1/3}+8x^{-1/3} is 6x^{4/3}+12x^{2/3}+C