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Question

solve: dx1+x+x2

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Solution

We are write denominator as
1+x+x2=1+14+2.12.x+x214=34+(12+x)2
11+x+x2dx=134+(x+12)2dx
=134[1+43(x+12)2]dx=4311+[23+(x+12)]2dx
=4311+(23x+13)2dx=43.32231+(2x3x+13)2dx
=23arctan(2x3x+13)=23arctan(2x+13)Ans.


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