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Evaluate: int1/(x^2+6x+5)dx...

Evaluate: `int1/(x^2+6x+5)dx`

Text Solution

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`int(1)/(2x^(2)+x-1)dx`
`=(1)/(2)int(1)/(x^(2)+(x)/(2)-(1)/(2))dx`
`=(1)/(2)int(1)/((x+1//4)^(2)-(3//4)^(2))dx`
`=(1)/(2)*(1)/(2(3//4))log|(x+1//4-3//4)/(x+1//4+3//4)|+C`
`=(1)/(3)log|(x-1//2)/(x+1)|+C=(1)/(3)log|(2x-1)/(2(x+1))|+C`
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