∫ dx/(1+2tanx)= ∫ cosx/(cosx+2sinx) dx= (1/5)∫ dx + (2/5)∫ (2cosx-sinx)/(cosx+2sinx) dx= (1/5)x + (2/5)∫ d(cosx+2sinx)/(cosx+2sinx) dx= (1/5)x + (2/5)ln|cosx+2sinx| + CNote：cosx = A(cosx+2sinx) ...