Complicated integral... or is it?

Calculus Level 3

Evaluate:

πe2ln(π)sin((x3πx)ln(x2+1))ex4+πcos(3x)dx\large \int_{- \pi}^{e^{2 \ln(\sqrt{\pi})}} \frac{\sin \left( (x^3 - \pi x) \ln(x^2+1) \right)}{e^{-x^4+\pi} \cos(3x)} dx

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