Evaluate $$\,\int\limits_0^\pi {{e^{\left| {\cos x} \right|}}} \left( {2\sin \left( {{1 \over 2}\cos x} \right) + 3\cos \left( {{1 \over 2}\cos x} \right)} \right)\sin x\,\,dx$$
Answer
$${{24} \over 5}\left[ {e\cos \left( {{1 \over 2}} \right) + {1 \over 2}e\sin \left( {{1 \over 2}} \right) - 1} \right]$$