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Question

If the integrals of the function sin2x1+cosx is ax+bsinx.
Find a+b.

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Solution

sin2x1+cosx=(2sinx2cosx2)22cos2x2

=4sin2x2cos2x22cos2x2
=2sin2x2=1cosx
sin2x1+cosxdx=(1cosx)dx
=xsinx+C

a+b=1+(1)=0

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