What is the integral of (1-x^{-1/3}) ?

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

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integral of (1-x^{-1/3})

\int (1 - x^{- \frac{1}{3}}) d x

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

Solution steps

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

\int 1 d x = x

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

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

Add a constant to the solution

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

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