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Question

Evaluate : cos1xx2dx

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Solution

Put cos1x=t
x=cost
dx=sintdt

cos1xx2dx=tcos2t(sint)dt

=tI(sect.tant)dtII

=t.sect1.sectdt

=tsect+log|sect+tant|+c

=tcost+log1+sintcost+c

=cos1xx+log1+sin(cos1x)x+c

=cos1xx+log1+1x2x+c

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