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Example 1 Evaluate da1+3sin2xdxSolution: Let21+3sin xDivide numerator and denominator by cos2 x, we getsec2 x dxsecx+3 tan2 x2sec xdx1+4 tan2xLettan x = tsec" xdx = dtdt 1!=f_a_ =-tan-1 (2)=-tan-1 (2 tan x)+c

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