原式=∫ln(x+x^3)dx
=xln(x+x^3)-∫xdln(x+x^3)
=xln(x+x^3)-∫x*1/(x+x^3)*(1+3x^2)dx
=xln(x+x^3)-∫(1+3x^2)/(1+x^2)dx
=xln(x+x^3)-∫[3-2/(1+x^2)]dx
=xln(x+x^3)-3x+2arctanx+C