exo7 5443

$f_1(x)=\frac{1+x^2}{x^3}(\Arctan x-\frac{x}{1+x^2})$.

$f_2(x)=|\tan x|+\cos x$.

$f_3(x)=x-\ln\left|\frac{120+60x+12x^2+x^3}{120-60x+12x^2-x^3}\right|$.

$4_(x)=xe^{\frac{2x}{x^2-1}}$.

$f_5(x)=\frac{1}{x}\ln\left(\frac{e^x-1}{x}\right)$.

$f_6(x)=x+\sqrt{|x^2-1|}$.

$f_7(x)=e^{/\ln x}$.

$f_8(x)=\left(1+\frac{1}{x}\right)^x$.

$f_9(x)=\mbox{log}_2(1-\mbox{log}_{\frac{1}{2}}(x^2-5x+6))$.

$f_{10}(x)=E(x)+(x-E(x))^2$.

$f_{11}(x)=\Arcsin\sqrt{\frac{1}{2}-x}+\Arcsin\sqrt{\frac{1}{2}+x}$.

$f_{12}(x)=\frac{\Arcsin x}{x}$.

$f_{13}(x)=e^{1/x}\sqrt{x+4}$.

$f_{14}(x)=\Arccos(\frac{1}{\ch x})$.

$f_{15}(x)=\ln(y+\sqrt{y^2-1})-\ln(\frac{1+x}{1-x})$ où $y=\frac{1+x^2}{1-x^2}$.

$f_{16}(x)=\ln|\sh x-1|$.

$f_{17}(x)=x^{(x^x)}$.

$f_{18}(x)=(\cos x+\sin x)^{1/x}$.

$f_{19}(x)=\sqrt[3]{x^3+1}-\sqrt{x^2-1}$.

$f_{20}(x)=\Arcsin(2x-1)+2\Arctan\sqrt{\frac{1-x}{x}}$.

$f_{21}(x)=\ln(\ch x)$.

$f_{22}(x)=3^{2x-1}-5.3^{x-1}-x\ln3$.

$f_{23}(x)=\ln\left|\frac{1}{e^x-1}\right|$.