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Let  x2nπ1,nN The indefinite integral  x2sinx2+1sin2x2+12sinx2+1+sin2x2+1 is but for an arbitrary constant 

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a
log12secx2+1
b
logsecx2+12
c
12logsecx2+1
d
none of these 

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detailed solution

Correct option is B

We have 

x2sinx2+1sin2x2+12sinx2+1+sin2x2+1dx=x2sinx2+12sinx2+1cosx2+12sinx2+1+2sinx2+1cosx2+1dx=x1cosx2+11+cosx2+1dx=xtanx2+12dxtanx2+12dx2+12=logsecx2+12+C

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