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Calculus Level 3

If \(\cos x = \large{\frac{\sqrt{16 - \pi^2}}{4}}\) and \(\sin x = a\), when \(a > 0\), find the value of: \[4\int{at^e}\, dt, \]

where \(e\) is a constant.

Clarification: \(C\) denotes the arbitrary constant of integration.

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