Find the integral

Calculus Level pending

\[\int_{-1}^{1} \left (\frac{\mathrm{d^{700}} }{\mathrm{d} x^{700}} \left [ (x^{2}-1)^{700} \right ] \right ) \sum_{k=0}^{4} (-1)^{k} \begin{pmatrix} 8\\ k \end{pmatrix} \begin{pmatrix} 16-2k\\ 8 \end{pmatrix} x^{8-2k} \; \mathrm{d}x \]

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