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Question

π/20tanx1+m2tan2xdx


Solution

= π/20tanx1+m2tan2xdx=π/20sinxcosx1+m2.sin2xcos2xdx=π/20sinxcosxcos2x+m2sin2xcos2xdx=π/20sinx cosx1sin2x+m2sin2xdx=π/20sinx cosx1sin2x(1m2)Putsin2x=t2 sinx cosx dx=dtI=1210dt1t(1m2)=12[log|1t(1m2)|11m2]10=12[log|m2|.11m2]=logm(m21)=log mm21

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