My fifth integral problem

Calculus Level 4

\[ \large \displaystyle \int_{-3}^{1} \sqrt{x^{2} + \sqrt{4x^{2} + \sqrt{16x^{2} + \sqrt{64x^{2} + \cdots}}}} \, dx = \, ? \]

Clarification: The coefficient of \(x^2\) in each successive nested radical is in the form of \(4^{n-1} \), where \(n\) is a positive integer.

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