Question

求高数习题详细解答过程！急！

Answer 1

∫arctanx dx
=xarctanx-∫x darctanx
=xarctanx-∫x/(1+x²) dx
=xarctanx-(1/2)*∫d(1+x²)/(1+x²)
=xarctanx-(1/2)*ln(1+x²)+C

追答

用分部积分

题目看错了，等一下

∫xArctanx dx
=1/2积分:arctanxdx^2
=x^2/2arctanx-1/2积分:x^2d(arctanx)
=x^2/2arctanx-1/2积分:x^2/(1+x^2)dx
=x^2/2arctanx-1/2积分:(x^2+1-1)/(1+x^2)dx
=x^2/2arctanx-x/2+arctanx+C

Answer 2