integration root under 1 + cos 2 X into DX is equal to
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√1+cos2x =√2 cosx
because cos2x = 2cos^2x - 1
then
integration (√2 cosx )dx = √2 sinx+ constant
because cos2x = 2cos^2x - 1
then
integration (√2 cosx )dx = √2 sinx+ constant
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