公式打不上,发图得审查……思路是:令x=tan α ,可以化简为:(cosα)^2的积分,(cosα)^2=(1+cos 2α)/2最终=x/2+1/4*sin(2x) +C
∫1/(1+X²)²dx=∫(1+x²-1)/(1+X²)²dx=∫1/(1+X²)dx-∫x²/(1+X²)²dx=arctanx+1/2∫xd1/(1+X²)=arctanx+1/2(x/(1+x²)-∫1/(1+X²)dx)=1/2arctanx+x/(2(x²+1))+C