Astro? No! Asteroid!

Calculus Level 2

01(1x9995)1/1999dx01(1x1999)1/9995dx= ? \large \frac{ \displaystyle \int_0^1 (1-x^{9995})^{1/1999} \, dx } { \displaystyle \int_0^1 (1-x^{1999})^{1/9995} \, dx } = \ ?

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