∫ln(x^2+1)dx 分部积分
=xln(x^2+1)-∫2x^2dx/(x^2+1)
=xln(x^2+1)-2∫(x^2+1-1)dx/(x^2+1)
=xln(x^2+1)-2∫(1-1/(x^2+1))dx
=xln(x^2+1)-2x+2arctanx+C
∫ln(x^2+1)dx 分部积分
=xln(x^2+1)-∫2x^2dx/(x^2+1)
=xln(x^2+1)-2∫(x^2+1-1)dx/(x^2+1)
=xln(x^2+1)-2∫(1-1/(x^2+1))dx
=xln(x^2+1)-2x+2arctanx+C