Mathematics

Mathematics

Problem

Evaluate ∫0πe∣cos⁡x∣(2sin⁡(12cos⁡x)+3cos⁡(12cos⁡x))sin⁡x dx\int_{0}^{\pi} e^{|\cos x|} \left( 2 \sin\left(\frac{1}{2} \cos x\right) + 3 \cos\left(\frac{1}{2} \cos x\right) \right) \sin x \, dx .

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