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Evaluate: int(2x+1)/(x^4+2x^3+x^2-1)dx...

Evaluate: `int(2x+1)/(x^4+2x^3+x^2-1)dx`

Text Solution

Verified by Experts

`I = int(2x+1)/(x^(4)+2x^(3)+x^(2)-1)dx`
`=int(2x+1)/((x^(2)+x)^(2)-1)dx`
Let `x^(2)+x=t`
`:. dt=(2x+1)dx`
`:. I=int(dt)/(t^(2)-1)`
`=(1)/(2)log_(e)|(x^(2)+x-1)/(x^(2)+x+1)|+C`
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