Integration through Branch Cut 0 to 1

This problem is very interesting ,here branch point is zero. here I mistook in one facts that artanx is equal to integration 0 to 1 (x/(1+(xy)^2) but I missed only x
branch cut method complex analysis
complex analysis branch cut
branch and cut method
branch cut examples
what is a branch cut in complex analysis
complex analysis branch
branch cut math
branch point complex analysis
#Branch_point_and_branch_cut_multivalued_functions_in_complex_analysis
#branch_points_and_branch_cut_Csir-NET_Gate_nbhm_tifr_by-Sunil_Bansal
#introducing_branch_points_and_branch_cuts_complex_variable
#integration_through_a_branch_cut