Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\left(x + 1\right) \operatorname{atan}{\left(x + 1 \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = -1$$
Numerical solution$$x_{1} = -0.999999483228915$$
$$x_{2} = -0.999999484804135$$
$$x_{3} = -0.999999486509974$$
$$x_{4} = -0.999999483628689$$
$$x_{5} = -1.00000051686884$$
$$x_{6} = -1.00000051628437$$
$$x_{7} = -1.00000030086633$$
$$x_{8} = -1.00000051708657$$
$$x_{9} = -0.999999483259633$$
$$x_{10} = -0.999999484087395$$
$$x_{11} = -1.0000005167933$$
$$x_{12} = -0.999999487357113$$
$$x_{13} = -1.00000051514264$$
$$x_{14} = -0.999999483200405$$
$$x_{15} = -0.999999483867896$$
$$x_{16} = -1.00000051653166$$
$$x_{17} = -0.999999483083971$$
$$x_{18} = -0.999999482933008$$
$$x_{19} = -1.00000051694914$$
$$x_{20} = -0.999999494031996$$
$$x_{21} = -1.00000051642109$$
$$x_{22} = -0.999999482998444$$
$$x_{23} = -1.00000050507963$$
$$x_{24} = -1.00000051703978$$
$$x_{25} = -1.00000051574465$$
$$x_{26} = -1.00000051709698$$
$$x_{27} = -0.999999482957244$$
$$x_{28} = -0.99999948290065$$
$$x_{29} = -0.999999483778329$$
$$x_{30} = -0.999999483969997$$
$$x_{31} = -1.00000051588532$$
$$x_{32} = -1.00000051706428$$
$$x_{33} = -1.00000051666271$$
$$x_{34} = -1.00000051647916$$
$$x_{35} = -1.00000051710693$$
$$x_{36} = -1.00000051538172$$
$$x_{37} = -0.999999482944834$$
$$x_{38} = -1.00000051611122$$
$$x_{39} = -0.999999483029772$$
$$x_{40} = -0.999999483292825$$
$$x_{41} = -0.999999483173877$$
$$x_{42} = -0.999999482881351$$
$$x_{43} = -1.00000051698267$$
$$x_{44} = -0.999999483410592$$
$$x_{45} = -1.00000050895384$$
$$x_{46} = -1.00000051110355$$
$$x_{47} = -1.00000051682024$$
$$x_{48} = -1.00000051705233$$
$$x_{49} = -1.0000005169981$$
$$x_{50} = -1.00000051689083$$
$$x_{51} = -0.999999488599745$$
$$x_{52} = -0.999999483367912$$
$$x_{53} = -0.999999483046795$$
$$x_{54} = -0.999999485442001$$
$$x_{55} = -0.999999482970283$$
$$x_{56} = -0.99999948589994$$
$$x_{57} = -1.00000051447572$$
$$x_{58} = -0.999999485086859$$
$$x_{59} = -0.999999484383777$$
$$x_{60} = -1.00000051600624$$
$$x_{61} = -1.00000051673309$$
$$x_{62} = -0.99999948422371$$
$$x_{63} = -0.999999482983998$$
$$x_{64} = -0.999999490564929$$
$$x_{65} = -1.0000005148477$$
$$x_{66} = -0.999999483457342$$
$$x_{67} = -1.00000051676433$$
$$x_{68} = -0.999999522095937$$
$$x_{69} = -0.999999484574183$$
$$x_{70} = -1.00000051669933$$
$$x_{71} = -1.00000051693086$$
$$x_{72} = -1.00000051657935$$
$$x_{73} = -0.999999483699156$$
$$x_{74} = -1.00000051635653$$
$$x_{75} = -0.999999482890793$$
$$x_{76} = -1.00000051334767$$
$$x_{77} = -1.00000051620319$$
$$x_{78} = -0.999999501301654$$
$$x_{79} = -1.00000051702659$$
$$x_{80} = -0.999999483125996$$
$$x_{81} = -0.99999948310432$$
$$x_{82} = -1.00000051557912$$
$$x_{83} = -1.00000051696638$$
$$x_{84} = -0.999999483565587$$
$$x_{85} = -0.99999948306483$$
$$x_{86} = -0.999999482921725$$
$$x_{87} = -1.0000005139937$$
$$x_{88} = -0.99999948301368$$
$$x_{89} = -1.00000047089392$$
$$x_{90} = -0.999999483149131$$
$$x_{91} = -0.999999639752099$$
$$x_{92} = -0.999999482910951$$
$$x_{93} = -1.00000051691146$$
$$x_{94} = -1.0000004966661$$
$$x_{95} = -1.00000051244353$$
$$x_{96} = -0.999999483328798$$
$$x_{97} = -0.999999483508765$$
$$x_{98} = -1.00000051707568$$
$$x_{99} = -1.00000051701271$$
$$x_{100} = -1.00000051684537$$
$$x_{101} = -1.00000051662286$$