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

1.	Evaluate:`int(x^2+1)/(x^4+x^2+1)dx`
Answer» We have `int((x^(2)-1))/((x^(4)+x^(2)+1))dx=int((1-(1)/(x^(2))))/((x^(2)+(1)/(x^(2))+1))dx` [ diving num . And denom . By `x^(2)` ] `=int((1-(1)/(x^(2))))/([(x+(1)/(x))^(2)-1])dx=int(dt)/((t^(2)-1))` `["Putting"(x+(1)/(x))=t and(1-(1)/(x^(2))dx=dt]` `=(1)/(2)log\|(t-1)/(t+1)\|+C=(1)/(2)log\|(x+(1)/(x)-1)/(x+(1)/(x)+1)\|+C` `=(1)/(2)log\|(x^(2)-x+1)/(x^(2)+x+1)\|+C`.

Discussion

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