被积函数分子分母除以x²有∫(x^2+1)/(x^4+1)dx=∫(1+1/x²)/(x²+1/x²)dx令u=x-1/x,则du=(1+1/x²)dx且u²=x²+1/x²-2则原式=∫du/(u²+2)=1/根号2*arctan(u/根号2)再u=x-1/x代进去
