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Let x21,nN.The value of x2sin x2+1sin 2x2+12sin x2+1+sin 2x2+1dx is equal to 

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a
log⁡12sec⁡x2+1+C
b
log ⁡sec⁡ x2+12+C
c
12log⁡ sec⁡ x2+1+C
d
None of the above

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detailed solution

Correct option is B

We have, ∫x2sin ⁡x2+1−sin⁡ 2x2+12sin ⁡x2+1+sin⁡ 2x2+1dx=∫x2sin⁡ x2+1−2sin⁡x2+1⋅cos ⁡x2+12sin ⁡x2+1+2sin⁡x2+1⋅cos ⁡x2+1dx=∫x1−cos ⁡x2+11+cos ⁡x2+1dx=∫xtan ⁡x2+12dx=∫tan ⁡x2+12dx2+12=log ⁡sec ⁡x2+12+C


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