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Question

Let f(x)=2sin2x1cosx+cosx(2sinx+1)(1+sinx) then ex(f(x)+f(x))dx where c is the constant of integration

A
extanx+C
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B
excotx+C
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C
ex cosec2x+C
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D
exsec2x+C
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Solution

The correct option is C extanx+C
We can write f(x)=2sin3x+2sin2xsinx12sin3xsin2x+2sinx+1cosx(1+sinx)
=sinx(1+sinx)cosx(1+sinx)=tanx
We know,ex(f(x)+f(x))=exf(x)+c=extanx+c

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