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Question

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

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Solution

Consider, I=x(x1)(x2+1)dx

=(12(x1)x12(x2+1))dx

=121x1dx12x1x2+1dx

=12log(x1)12[xx2+11x2+1]dx

=12ln(x1)12[ln(x2+1)2+tan1(x)]

=ln(x2+1)4+tan1x2+ln(x1)2+c



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