El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\left|{\log{\left(1 + \frac{1}{\sqrt[5]{x}} \right)} \operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{x} \right)}}\right| = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución numérica$$x_{1} = -3323.805027498$$
$$x_{2} = 62.8318530717959$$
$$x_{3} = 141.371669411541$$
$$x_{4} = -50.2654824574367$$
$$x_{5} = 84.8230016469244$$
$$x_{6} = -53.4070751110265$$
$$x_{7} = -3.14159265358979$$
$$x_{8} = -6.28318530717959$$
$$x_{9} = -18.8495559215388$$
$$x_{10} = 78.5398163397448$$
$$x_{11} = -75.398223686155$$
$$x_{12} = -9.42477796076938$$
$$x_{13} = 72.2566310325652$$
$$x_{14} = -43.9822971502571$$
$$x_{15} = 31.4159265358979$$
$$x_{16} = 9.42477796076938$$
$$x_{17} = 40.8407044966673$$
$$x_{18} = -69.1150383789755$$
$$x_{19} = 12.5663706143592$$
$$x_{20} = 87.9645943005142$$
$$x_{21} = 59.6902604182061$$
$$x_{22} = -37.6991118430775$$
$$x_{23} = -100.530964914873$$
$$x_{24} = -91.106186954104$$
$$x_{25} = 97.3893722612836$$
$$x_{26} = 18.8495559215388$$
$$x_{27} = -12.5663706143592$$
$$x_{28} = -78.5398163397448$$
$$x_{29} = 34.5575191894877$$
$$x_{30} = -94.2477796076938$$
$$x_{31} = 367.566340470006$$
$$x_{32} = 43.9822971502571$$
$$x_{33} = -4602.43323750905$$
$$x_{34} = -31.4159265358979$$
$$x_{35} = -333.008821280518$$
$$x_{36} = -65.9734457253857$$
$$x_{37} = 75.398223686155$$
$$x_{38} = 56.5486677646163$$
$$x_{39} = -81.6814089933346$$
$$x_{40} = 3.14159265358979$$
$$x_{41} = 15.707963267949$$
$$x_{42} = -56.5486677646163$$
$$x_{43} = -21.9911485751286$$
$$x_{44} = 50.2654824574367$$
$$x_{45} = -15.707963267949$$
$$x_{46} = 28.2743338823081$$
$$x_{47} = -1533.09721495182$$
$$x_{48} = 94.2477796076938$$
$$x_{49} = -323.584043319749$$
$$x_{50} = 204.203522483337$$
$$x_{51} = -59.6902604182061$$
$$x_{52} = -546.637121724624$$
$$x_{53} = -34.5575191894877$$
$$x_{54} = -97.3893722612836$$
$$x_{55} = 21.9911485751286$$
$$x_{56} = 65.9734457253857$$
$$x_{57} = 37.6991118430775$$
$$x_{58} = -87.9645943005142$$
$$x_{59} = -72.2566310325652$$
$$x_{60} = -25.1327412287183$$
$$x_{61} = -28.2743338823081$$
$$x_{62} = 81.6814089933346$$
$$x_{63} = 6.28318530717959$$
$$x_{64} = 100.530964914873$$
$$x_{65} = -131.946891450771$$
$$x_{66} = -15334.1137421718$$
$$x_{67} = 53.4070751110265$$
$$x_{68} = -47.1238898038469$$