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int(0)^(1) x e^(x) dx=1...

`int_(0)^(1) x e^(x) dx=1`

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`int_(0)^(1) xe^(x) dx=[x int e^(x) dx-int 1.e^(x) dx]_(0)^(1)`
`=[xe^(x) -e^(x)]_(0)^(1)=[e^(x)(x-1)]_(0)^(1)`
`=e(1-1)-e^(0)(0-1)=0+1=1`
Hence proved.
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