# A definite integral which shows us how close our approximation is to a transcendental number.

Calculus Level 4

$\large \int_0^1 \frac {x^4(1-x)^4}{1+x^2} dx=A$

The equation above holds true for real number $A$. What is $\lceil 10000A\rceil$?

Notation: $\lceil \cdot \rceil$ denotes the ceiling function.

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