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sinxsin(xa)dx=

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a
xsina+cosalogsinx−a+C
b
cosx+sinxlogsinx−a+C
c
(x−a)cosa+sinalogsin(x−a)+C
d
xcosa+sinalogsin(x−a)+C

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detailed solution

Correct option is D

I=∫sinxsin(x−a)dx=∫sin⁡(x−a+a)sin⁡(x−a)dx=∫sin⁡(x−a)cos⁡a+cos⁡(x−a)sin⁡asin⁡(x−a)dx=∫[cos⁡a+sin⁡acot⁡(x−a)]dx=cos⁡a∫dx+sin⁡a∫cot⁡(x−a)dx=xcos⁡a+sin⁡alog⁡|sin⁡(x−a)|+C


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