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Question

Evaluate : x1x21+x2dx.

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Solution

GivenI=x1x21+x2dxLetx2=t2xdx=dtxdx=dt2ThenI=1t1+tdt2=121t1t2dt=12dt1t212tdt1t2Lett=sinθdt=cosθdθ=12cosdθcosθ12sinθcosθcosθdθ=12dθ12cosθdθ=12θ12sinθ+C=12(sin1tt)+C=12(sin1x2x2)+C

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