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Question

xsin1xdx=1k(1x2x+(px21)sin1x).Find k+p ?

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Solution

I=xsin1xdx
=12x2sin1x12x21x2dx.
Substitute x=sinudx=cosudu
I=12x2sin1x12sin2udu
=12x2sin1x+14cos2udu14du
=12x2sin1x+sin2u8u4
=14(1x2x+(2x21)sin1x)
k+p=6

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