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Question

Show that x(1x21+x2)dx=[sin1x2+1x4].

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Solution

Let I=x1x21+x2dx
Put t=x2dt=2xdx
I=121tt+1dt
Put s=1tt+1ds=(1t(t+1)21t+1)dt
I=s(s1)2ds
Put p=sdp=12sdx
I=2p2(p21)2dp=2(1p2+11(p2+1)2)dp=tan1p+sin(tan1p)cos(tan1p)
Therefore I=12(1x21+x2tan11x21+x2)

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