求不定积分（arctanx）平方的不定积分怎么算啊?

Question

求不定积分
（arctanx）平方的不定积分怎么算啊?

Answer 1

原式=x(arctanx)^2-∫[x2arctanx(1/1+x^2)]dx
=x(arctanx)^2+∫arctanx(d1+x^2/1+x^2)
=x(arctanx)^2+∫arctanx*2d(1+x^2)
=x(arctanx)^2+2[(1+x^2)arctanx-(1+x^2)*(1/1+x^2)]
=x(arctanx)^2+2(1+x^2)arctanx-2x+c