∫1/﹙1+x²﹚xdx

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∫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)/[

∫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