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Question

Solve the problem:-
xsin1xdx

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Solution

I=xsin1xdx
Let u=sin1xdu=dx1x2

I=x22sin1xx221x2dx [using ILATE rule]
I=x22sin1x12x21x2dx
I=x22sin1x121(1x2)1x2dx
I=x22sin1x12dx1x2+12(1x2)dx1x2
I=x22sin1x12sin1x+12(1x2)112dx
I=x22sin1x12sin1x+12(1x2)12dx
I=x22sin1x12sin1x+12(x21x2+12sin1x)+c using 1x2dx=x21x2+12sin1x
I=x22sin1x12sin1x+14x1x2+14sin1x+c
I=x22sin1x24sin1x+14x1x2+14sin1x+c
I=x22sin1x14sin1x+14x1x2+c

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