1).分子变为x+2-1
原式=∫1/(x+2)-1/(x+2)²dx=ln|x+2|+1/(x+2)+c
2).分子变为2x+2+1,2x+2dx=x²+2x+2原式=∫(2x+2)/(x²+2x+2)+1/((x+1)²+1)dx=ln(x²+2x+2)+arctan(x+1)+c
3).可以设原被积函数=A(2x-1)/(x²-x+1)+B/(x+2)+C/(x²-x+1)
原积分=Aln(x²-x+1)+Bln|x+2|+2/√3*C*arctan((2x-1)/√3)+c
用待定系数法求出A=2/7,B=-4/7,C=-3/7即可求出原函数
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