Integrate[6x(3x-1)^(-1/3),x] - Wolfram|Alpha

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Indefinite integral

integral6 x (3 x - 1)^(-1/3) dx = 3/5 (2 x + 1) (3 x - 1)^(2/3) + constant

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Expanded form of the integral

6/5 (3 x - 1)^(2/3) x + 3/5 (3 x - 1)^(2/3) + constant

Series expansion of the integral at x=0

piecewise | 3/5 (-1)^(2/3) - 3 (-1)^(2/3) x^2 - 2 (-1)^(2/3) x^3 - 3 (-1)^(2/3) x^4 - 28/5 (-1)^(2/3) x^5 + O(x^6) | Im(x)>=0
-3/10 i (sqrt(3) + -i) + 3/2 (1 + i sqrt(3)) x^2 + (1 + i sqrt(3)) x^3 + 3/2 (1 + i sqrt(3)) x^4 + 14/5 (1 + i sqrt(3)) x^5 + O(x^6) | (otherwise)

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Series expansion of the integral at x=1/3

3^(2/3) (x - 1/3)^(2/3) + 6/5 3^(2/3) (x - 1/3)^(5/3) + O((x - 1/3)^(37/3))
(Puiseux series)

Big‐O notation »

Series expansion of the integral at x=∞

6/5 3^(2/3) x^(5/3) + x^(2/3)/3^(1/3) + O((1/x)^(1/3))
(Puiseux series)

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