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int(0)^(1)x e^(x^(2)) dx...

`int_(0)^(1)x e^(x^(2)) dx`

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`" Let I=" int_(0)^(1) xe^(x^(2))dx`
`"Let "x^(2)=trArr 2x=(dt)/(dx) rArr xd x= (dt)/(2)`
`x=0rArr t=0 `
`"and " x=1 rArr t=1`
` :, I=(1)/(2) int_(0)^(1) e^(t) dt=(1)/(2)[e^(t)]_(0)^(1)`
`=(1)/(2)(e^(1)-e^(0))=(1)/(2)(e-1)`
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