An Annoying Rational Function

Calculus Level 3

01x4(1x2)5(1+x2)10dx=A\int_0^1\frac{x^4\left(1-x^2\right)^5}{\left(1+x^2\right)^{10}}\, dx=A

Given the above, find 1A.\frac{1}{A}.

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