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∫(x + sin x)/(1 + cos x) dx is equal to

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⇒ ∫(2t+2t tan2 t+2 tan t) dt=2∫(t + t tan^2 t+ tan t) dt

⇒ 2∫tdt+2∫t (sec2(t-1)dt+2∫tan t dt

⇒ 2∫tdt+2∫t sec2 t dt-2∫tdt+2∫tan t dt

⇒ 2∫t sec2 t dt+2∫tant dt ….(1)

Applying Integration by parts on ∫t sec2 t dt

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