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∫0π/2exsinxcosx dx\large \int_{0}^{\pi /2} e^x\sin x\cos x \, dx∫0π/2exsinxcosxdx
If the above integral can be expressed asa+ebπ/cd, \large \dfrac{a+{e^{{b\pi} / {c}}}}{d} , da+ebπ/c, where a,b,ca,b,ca,b,c and ddd are positive integers with bbb and ccc coprime, find the value of a+b+c+da+b+c+da+b+c+d.
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