JEE MAINS 2018 integrate `int_0^(2pi) e^x . sin (pi/4 + x/2) dx`

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If the Integral of [sin 2πx]/e^x-[x] dx from 0 to 10 = αe^(-1)+ βe^-1/2+γ, where α,β,γ are integers If the Integral of [sin 2πx]/e^x-[x] dx from 0 to 10 = αe^(-1)+ βe^-1/2+γ, where α,β,γ are integers