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Question

If x4+1x(x2+1)2dx=Aln|x|+B1+x2+C, where C is the constant of integration, then |A+B| is equal to

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Solution

Let I=x4+1x(x2+1)2dx
=(x2+1)22x2x(x2+1)2dx
=1xdx2x(x2+1)2dx
=ln|x|+11+x2+C
A=1,B=1
|A+B|=2

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