Evaluate :
[tex] \int \limits_ {0}^{\pi} {e}^{ | \cos x| }[ \: 3 \cos( \frac{1}{2} \cos x) + 2 \sin \: ( \frac{1}{2} \cos x)] \sin x \: dx \\ [/tex]
[tex] \int \limits_ {0}^{\pi} {e}^{ | \cos x| }[ \: 3 \cos( \frac{1}{2} \cos x) + 2 \sin \: ( \frac{1}{2} \cos x)] \sin x \: dx \\ [/tex]
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