Solve it without use $\text{'}$H$$pital$\text{'}$s rule

Show that :

$\underset{x0}{lim}\frac{x^2{e}^x+2^x-\frac{2^{x}si{n}^{-1}(x)}{x}+\frac{1}{co{t}^2(x)}-x^2-se{c}^2(-x)+\frac{si{n}^{-1}(x)}{x}}{x^{ln}+x^2{2}^x+co{s}^2(si{n}^{-1}(x))-(\underset{t0}{lim}\frac{ta{n}^{-1}(t)}{t})-{}^{lnx}}$

$=\frac{6-ln2}{ln(64)}$