A calculus problem by Akeel Howell

Calculus Level 4

Let \( f: \mathbb{R} \mapsto \mathbb{C}\) be defined as \(\displaystyle{ f(x) = \int{\pi e^{2\arcsin(x)}}dx} \space\) and \( f(0) = \dfrac{2\pi}{5}\).

Find \(|f(3)|\).

If your answer is of the form \(\dfrac{\sqrt{b}}{a}\pi e^{\pi}\), where \(a\) and \(b\) are prime numbers, find \(a+b\).

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