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Methods of integration

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Question

Let x21,nN . If x2sinx2+1sin2x2+12sinx2+1+sin2x2+1dx=lnf(x)+C then sec1f(1) equals

Moderate
Solution

Let x2+1=txdx=dt2

Given integral =122sint2sintcost2sint+2sintcostdt

=12tant2dt=lnsect2+Cf(x)=secx2+12sec1f(1)=1


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