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Evaluate : int(0)^(4)x.e ^(2x) dx...

Evaluate : `int_(0)^(4)x.e ^(2x) dx`

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`int_(0)^(4)x.e ^(2x) dx`
`=[x.(e^(2x))/(2)]_(0)^(1) -int_(0)^(1)1. (e^(2x))/(2)dx`
`=1/2 [e^(2)-0] -1/4 [e^(2x)]_(0)^(1)`
`=1/2 e^(2) -1/4(e^(2)-1)`
`=1/4 e^(2) +1/4 =1/4(e^(2)+1). `
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