原式=∫x^3dx/(x^4+2x^2+5)
=(1/4)∫d(x^4+2x^2+5)/(x^4+2x^2+5)
-∫xdx/(x^4+2x^2+5)
=(1/4)ln|x^4+2x^2+5|
-∫d[(x^2+1)/2]/4{1+[(x^2+1)/2]^2}
=(1/4)ln|x^4+2x^2+5|
-(1/4)arctan[(1+x^2)/2]+C