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prove thatint0^(102)(x-1)(x-2)..(x-100)x...

prove that`int_0^(102)(x-1)(x-2)..(x-100)xx1/(1/(x-1)+1/(x-2)+. .1/(x-100))dx=101 !-100 !`

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The correct Answer is:
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`I=int_(0)^(102)(x-1)(x-2)……(x-100)`
`xx(1/((x-1))+1/((x-2))+…+1/((x-100)))dx`
`-int_(0)^(102)d/(dx)((x-1)(x-2)………(x-100))dx`
`=[(x-1)(x-2)…………(x-100)]_(0)^(102)`
`=101!-100!`
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