Integration on an (Integration on a Limit)

Calculus Level 5

If

\[\displaystyle \int_1^5 \int_1^x \lim_{z \rightarrow y} \frac{z^5+z^4}{z^3+1} \mathrm {d}x \mathrm {d}y\]

is equivalent to \((a \times \tan^{-1}(b) + c\pi + d \times \ln (e) + f)(\frac {x-g}{h})\), find the value of the digit sum of \(a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 + h^2\).

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