Simplify[Integrate[Exp[x^(-2)]/x^3,{x,1,2}]]
N[%]

f[x_]:=2+2/5*x
g[x_]:=8(x/15)^2
Plot[{g[x],f[x]},{x,-2,15},AspectRatio->1.1]
Integrate[f[x]-g[x],x]
Integrate[f[x]-g[x],{x,0,15}]
Integrate[Pi*(f[x]^2-g[x]^2),{x,0,15}]

Solve[Log[x^2+1]−2 Log[x]==1,x]
Simplify[Log[10,Sqrt[40]]] (* Wow! *)

f[x_]:=4/(1+Exp[3x]) -2
g[x_]:=1/3*Log[4/(x+2)-1]
Plot[f[x],{x,-2,2},AspectRatio->1.1]
Plot[{f[x],g[x]},{x,-2,2},PlotRange->{{-2,2},{-2,2}},AspectRatio->1.3]