求2x(x^2+1)arctanx的不定积分

原式=∫(x²+1)arctanxd(x²+1)
=1/2∫arctanxd(x²+1)²
=1/2*(x²+1)²arctanx-1/2∫(x²+1)²darctanx
=1/2*(x²+1)²arctanx-1/2∫(x²+1)²*1/(x²+1) dx
=1/2*(x²+1)²arctanx-1/2∫(x²+1)dx
=1/2*(x²+1)²arctanx-1/2*(x³/3+x)+C