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Question

Find the integrals of the functions cosx1+cosx

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Solution

cosx1+cosx=cos2x2sin2x22cos2x2
=12[1tan2x2]
cosx1+cosxdx=12(1tan2x2)dx
=12(1sec2x2+1)dx
=12(2sec2x2)dx
=122xtanx212+C
=xtanx2+C

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