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int(2)^(3) (x dx)/(x^(2)+1)...

`int_(2)^(3) (x dx)/(x^(2)+1)`

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`"Let I "=int_(2)^(3)(x)/(x^(2)+1)dx`
`underset(rArr" "2x dx=dt rArr x dx=(dt)/(2))(" Let " x^(2)+1=t)`
x=2 then t =5 and x=3 then t=0
`I=(1)/(2)int_(0)^(10) (1)/(t) dt=(1)/(2)[log |t|]_(5)^(10)`
`=(1)/(2)[log |10log |5|]`
`=(1)/(2)log|(10)/(5)|=(1)/(2)log 2`
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