∫ln﹙x²＋1﹚dx
=xln(x²＋1)-∫[2x²/﹙x²＋1﹚]dx
=xln(x²＋1)-2∫[1-1/﹙x²＋1﹚]dx
=xln(x²＋1)-2x+2arctanx+ c