Evaluate:`int1/(2x^2+x-1)dx`

1.	Evaluate:`int1/(2x^2+x-1)dx`
Answer» We have `int(dx)/((2x^(2)+x-1))=(1)/(2)int(dx)/((x^(2)+(1)/(2)x-(1)/(2)))` `=(1)/(2)int(dx)/([{x^(2)+(1)/(2)x+((1)/(2))^(2)}-(1)/(16)-(1)/(2)])=(1)/(2)int(dx)/([(x+(1)/(4))^(2)-((3)/(4))^(2)])` `=(1)/(2)(1)/(2*(3)/(4))log\|((x+(1)/(4))-(3)/(4))/((x+(1)/(4))+(3)/(4))\|+C=(1)/(3)log\|(2x-1)/(2(x+1))\|+C`

Discussion

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