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Evaluate: ∫ e^2x (1 + sin 2x/ 1 + cos 2x) dx

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Evaluate: ∫ e2x (1 + sin 2x/ 1 + cos 2x) dx

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The given integral is

= ∫ e2x ((1/2) sec2 x + tan x) dx 

= (1/2) ∫ e2x (sec2 x + 2tan x) dx 

= (1/2) ∫ e2x (2 tan x + sec2 x) dx 

= (e2x 2tan x/ 2)  + c 

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