∵∫arctanxx2(1+x2)dx=∫arctanx(1x2−11+x2)dx=∫arctanxx2dx−∫arctanx1+x2dx=−∫arctanxd(1x)−∫arctanxd(arctanx)=−1xarctanx+∫  1x(1+x2)dx−12(arctanx)2=−1xarctanx+∫(1x−x1+x2)dx−12(ar...