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Question

x2+1x4-x2+1 dx

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Solution

We have,I=x2+1x4-x2+1dxDividing numerator and denominator by x2I=1+1x2x2+1x2-1dx=1+1x2dxx2+1x2-2+1=1+1x2dxx-1x2+1Putting x-1x=t1+1x2dx=dtI=dtt2+12=tan-1t+C=tan-1x-1x+C=tan-1 x2-1x+C

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