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Question

Evaluate: x+3(x1)(x2+1)dx

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Solution

Let x+3(x1)(x2+1)=Ax1+Bx+Cx2+1
A(x2+1)+(Bx+C)(x1)=x+3
on solving this we get A=2,B=2,C=1
x+3(x3)(x2+1)dx=2dxx12xdxx2+1dxx2+1=2ln(x1)ln(x2+1)tan1x+C

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