sin(2x)+lg(2-x^2)>3 desigualdades

Se da la desigualdad:
$$\log{\left(2 - x^{2} \right)} + \sin{\left(2 x \right)} > 3$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\log{\left(2 - x^{2} \right)} + \sin{\left(2 x \right)} = 3$$
Resolvemos:
$$x_{1} = 30.9709781197208 - 1.14362805796399 i$$
$$x_{2} = -16.9256476650297 - 1.04325035471186 i$$
$$x_{3} = -35.6664918991943 - 1.16613269807171 i$$
$$x_{4} = 74.8675264956037 + 1.2756076403386 i$$
$$x_{5} = -79.575418064595 + 1.28393584031971 i$$
$$x_{6} = 49.7690784487077 + 1.21720048485761 i$$
$$x_{7} = 15.3730287535135 - 1.02707299086386 i$$
$$x_{8} = -38.7986913019341 + 1.17931477907617 i$$
$$x_{9} = -57.6098688239352 - 1.23866081566818 i$$
$$x_{10} = -98.4103799944213 + 1.31216861648377 i$$
$$x_{11} = -70.1600902571238 - 1.26662763278734 i$$
$$x_{12} = -38.7986913019341 - 1.17931477907617 i$$
$$x_{13} = 34.1009041977499 + 1.15902920159311 i$$
$$x_{14} = 65.4531932624499 + 1.25689638876599 i$$
$$x_{15} = -45.0662907477555 - 1.20230150555011 i$$
$$x_{16} = 59.1783592249404 + 1.24253619889075 i$$
$$x_{17} = 99.9801514690798 - 1.31422421694271 i$$
$$x_{18} = -88.9923132941104 + 1.29894890348751 i$$
$$x_{19} = -76.4367766937993 - 1.27845177989006 i$$
$$x_{20} = -7.68648040912541 + 0.919519366820738 i$$
$$x_{21} = 12.2784427200607 - 0.989858909842456 i$$
$$x_{22} = -67.0220929547887 + 1.26023063547622 i$$
$$x_{23} = -54.4731952889316 - 1.23051908226707 i$$
$$x_{24} = -73.2983267499914 - 1.27269122368535 i$$
$$x_{25} = -60.7469427605166 + 1.24629106829934 i$$
$$x_{26} = 81.1448045030949 - 1.28658158163 i$$
$$x_{27} = 93.7012192825989 + 1.30575792294369 i$$
$$x_{28} = 84.2836982565171 + 1.29169373797024 i$$
$$x_{29} = 37.2324336384428 - 1.17288465122069 i$$
$$x_{30} = 6.18240688286467 - 0.89286894786484 i$$
$$x_{31} = -45.0662907477555 + 1.20230150555011 i$$
$$x_{32} = 106.259467413807 + 1.32207596132869 i$$
$$x_{33} = 52.9050279590293 - 1.22623636389836 i$$
$$x_{34} = 15.3730287535135 + 1.02707299086386 i$$
$$x_{35} = 49.7690784487077 + 1.21720048485761 i$$
$$x_{36} = 87.4227406288751 + 1.29658268206625 i$$
$$x_{37} = 24.718022361291 - 1.10675787477096 i$$
$$x_{38} = -32.5357152914915 - 1.15154045305922 i$$
$$x_{39} = 78.0060747012707 - 1.2812268456937 i$$
$$x_{40} = -95.2709128193393 - 1.30793693548162 i$$
$$x_{41} = 46.6337173072421 + 1.2074641069121 i$$
$$x_{42} = -20.0379297021965 + 1.07168794730009 i$$
$$x_{43} = -26.2801754027456 + 1.11687586390649 i$$
$$x_{44} = 71.7291803094084 + 1.26969910796452 i$$
$$x_{45} = -1.93162194297013 + 0.826392422948605 i$$
$$x_{46} = -26.2801754027456 - 1.11687586390649 i$$
$$x_{47} = -51.3369855840383 - 1.22180023696161 i$$
$$x_{48} = 43.4990548204686 - 1.19692300125005 i$$
$$x_{49} = -63.8843651411369 - 1.25346527505305 i$$
$$x_{50} = 59.1783592249404 - 1.24253619889075 i$$
Descartamos las soluciones complejas:
Esta ecuación no tiene soluciones,
significa que esta desigualdad se cumple siempre o no se cumple nunca
comprobemos
sustituimos con un punto arbitrario, por ejemplo

x0 = 0

$$\sin{\left(0 \cdot 2 \right)} + \log{\left(2 - 0^{2} \right)} > 3$$

log(2) > 3

signo desigualdades no tiene soluciones