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Question

x2+x+1x2-x+1 dx

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Solution

Let I=x2+x+1x2-x+1dxNow,x2-x+1x2+x+1 1 x2-x+1 - + - 2x Therefore,x2+x+1x2-x+1=1+2xx2-x+1x2+x+1x2-x+1 dx=dx+2x-1+1x2-x+1 dx=dx+2x-1x2-x+1 dx+dxx2-x+1=dx+2x-1 dxx2-x+1+dxx2-x+122-122+1=dx+2x-1 dxx2-x+1+dxx-122+322=x+ log x2-x+1+23 tan-1 2x-13+C

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