∫1／﹙1＋x²﹚xdx

∫1／﹙1＋x²﹚xdx
∫1／﹙1＋x²﹚xdx

∫1／﹙1＋x²﹚xdx
∫ 1/(x+x^3) dx
=∫ (1+x^2-x^2)/[x(1+x^2)] dx
=∫ (1+x^2)/[x(1+x^2)] dx-∫ x^2/[x(1+x^2)] dx
=∫ 1/x dx-∫ x/(1+x^2) dx
=ln|x|-1/2∫ 1/(1+x^2) d(x^2)
=ln|x|-1/2ln(1+x^2)+C