Evaluate : `int_0^1(x e^(x)+sin(pix)/4)dx`

Explanation

Let `I=∫_0^1​(xe^x+sin(πx)/4​)dx`

`⇒∫(xe^x+sin(πx)/4)dx`


`=x∫e^xdx−∫{(dx)/(d​x)e^xdx}dx+{(​−cos(πx)/4)/(π/4)​​}`

`=xe^x−∫e^xdx−4/π​cos(πx)/4​`

`=xe^x−e^x−4/π​cos(πx)/4
`​

`=F(x)`

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