Question
Let f(x)=2sin2x−1cosx+cosx(2sinx+1)1+sinx then ∫ex(f(x)+f′(x))dx equals
(where c is the constant of integeration)
(where c is the constant of integeration)
Answer: Option A
:
A
cosx(1+2sinx)1+sinx−cos2x−sin2xcosx=cos2x(1+2sinx)−(1+sinx)(cos2x−sin2x)cosx(1+sinx)
=sinxcos2x+sin2x(1+sinx)cosx(1+sinx)=sinx(1−sinx)+sin2xcosx=tanx
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:
A
cosx(1+2sinx)1+sinx−cos2x−sin2xcosx=cos2x(1+2sinx)−(1+sinx)(cos2x−sin2x)cosx(1+sinx)
=sinxcos2x+sin2x(1+sinx)cosx(1+sinx)=sinx(1−sinx)+sin2xcosx=tanx
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