Symmetric Rearrangement

Calculus Level 5

01[(1x1/17)23+(1x1/23)17]dx\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 AB!C!40!A \frac{B!C!}{40!} for positive integers A,B,CA, B, C .

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

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