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Evaluate the following : int(1)^(2)(d...

Evaluate the following :
`int_(1)^(2)(dx)/(x^(2)+6x+5)`

Text Solution

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`int_(1)^(2)(dx)/(x^(2)+6x+5)`
`=int_(1)^(2)(dx)/((x^(2)+6x+9)-4)`
`=int_(1)^(2)(1)/((x+3)^(2)-(2)^(2))dx`
`=(1)/(2(2))[log|(x+3-2)/(x+3+2)|]_(1)^(2)`
`=(1)/(4)[log|(x+1)/(x+5)|]_(1)^(2)=(1)/(4)[log.(3)/(7)-log.(2)/(6)]`
`=(1)/(4)log((3)/(7)xx(6)/(2))=(1)/(4)log((9)/(7)).`
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