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I need some help with a multivalued complex integration problem.

Evaluate the integral of (x^2-x^3)^-(1/3) from 0 to 1.

I know you need to pick branches of the cube root function, and this will give you multiples of the integral which you can then equate to integrals along contours around the singularities 0 and 1. However, I'm having trouble finding those integrals around the contours. How can I use residues when fractional powers are involved? Any help is appreciated.

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# Integration of (x^2-x^3)^-(1/3) from 0 to 1

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