# Symmetric Rearrangement

Calculus Level 5

$\int _{ 0 }^{ 1 }{ { \bigg [ \left( 1-{ x }^{ 1/17} \right) }^{ 23 } } +{ \left( 1-{ x }^{ 1/23 } \right) }^{ 17 } \bigg ] dx$

The integral above is in the form $$A \frac{B!C!}{40!}$$ for positive integers $$A, B, C$$.

Calculate the smallest value of $$A \times B \times C \times 40$$.

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