Etude complète des fonctions suivantes
\(f_1(x)=\frac{1+x^2}{x^3}(\Arctan x-\frac{x}{1+x^2})\).
\(f_2(x)=|\tan x|+\cos x\).
\(f_3(x)=x-\ln\left|\frac{120+60x+12x^2+x^3}{120-60x+12x^2-x^3}\right|\).
\(4_(x)=xe^{\frac{2x}{x^2-1}}\).
\(f_5(x)=\frac{1}{x}\ln\left(\frac{e^x-1}{x}\right)\).
\(f_6(x)=x+\sqrt{|x^2-1|}\).
\(f_7(x)=e^{/\ln x}\).
\(f_8(x)=\left(1+\frac{1}{x}\right)^x\).
\(f_9(x)=\mbox{log}_2(1-\mbox{log}_{\frac{1}{2}}(x^2-5x+6))\).
\(f_{10}(x)=E(x)+(x-E(x))^2\).
\(f_{11}(x)=\Arcsin\sqrt{\frac{1}{2}-x}+\Arcsin\sqrt{\frac{1}{2}+x}\).
\(f_{12}(x)=\frac{\Arcsin x}{x}\).
\(f_{13}(x)=e^{1/x}\sqrt{x+4}\).
\(f_{14}(x)=\Arccos(\frac{1}{\ch x})\).
\(f_{15}(x)=\ln(y+\sqrt{y^2-1})-\ln(\frac{1+x}{1-x})\) où \(y=\frac{1+x^2}{1-x^2}\).
\(f_{16}(x)=\ln|\sh x-1|\).
\(f_{17}(x)=x^{(x^x)}\).
\(f_{18}(x)=(\cos x+\sin x)^{1/x}\).
\(f_{19}(x)=\sqrt[3]{x^3+1}-\sqrt{x^2-1}\).
\(f_{20}(x)=\Arcsin(2x-1)+2\Arctan\sqrt{\frac{1-x}{x}}\).
\(f_{21}(x)=\ln(\ch x)\).
\(f_{22}(x)=3^{2x-1}-5.3^{x-1}-x\ln3\).
\(f_{23}(x)=\ln\left|\frac{1}{e^x-1}\right|\).